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Topology optimization of freeform large-area metasurfacesFeb 08 2019We demonstrate optimization of optical metasurfaces over $10^5$--$10^6$ degrees of freedom in two and three dimensions, 100--1000+ wavelengths ($\lambda$) in diameter, with 100+ parameters per $\lambda^2$. In particular, we show how topology optimization, ... More

Sideways adiabaticity: Beyond ray optics for slowly varying metasurfacesJun 14 2018Nov 14 2018Optical metasurfaces (subwavelength-patterned surfaces typically described by variable effective surface impedances) are typically modeled by an approximation akin to ray optics: the reflection or transmission of an incident wave at each point of the ... More

Inverse design of large-area metasurfacesAug 13 2018Dec 14 2018We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) for applications such as multi-wavelength and multi-angle optimizations, and demultiplexers. To optimize ... More

Spectral projections of the complex cubic oscillatorOct 17 2013We prove the spectral instability of the complex cubic oscillator $-\frac{d^2}{dx^2}+ix^3+i\alpha x$ for non-negative values of the parameter $\alpha$, by getting the exponential growth rate of $\|\Pi_n(\alpha)\|$, where $\Pi_n(\alpha)$ is the spectral ... More

A Lagrangian approach for the compressible Navier-Stokes equationsJan 30 2012Sep 25 2014Here we investigate the Cauchy problem for the barotropic Navier-Stokes equations in R^n, in the critical Besov spaces setting. We improve recent results as regards the uniqueness condition: initial velocities in critical Besov spaces with (not too) \emph{negative} ... More

Noise-stability and central limit theorems for effective resistance of random electric networksJun 18 2012Mar 15 2016We investigate the (generalized) Walsh decomposition of point-to-point effective resistances on countable random electric networks with i.i.d. resistances. We show that it is concentrated on low levels, and thus point-to-point effective resistances are ... More

On the semi-classical analysis of Schrödinger operators with purely imaginary electric potentials in a bounded domainMay 23 2014In this paper, we describe the leftmost eigenvalue of the non-selfadjoint operator $\mathcal{A}_h = -h^2\Delta+iV(x)$ with Dirichlet boundary conditions on a smooth bounded domain $\Omega\subset\mathbb{R}^n\,$, as $h\rightarrow0\,$. $V$ is assumed to ... More

Periods and Reciprocity ISep 27 2018Apr 24 2019Given $\mathbf{F}$ a number field with ring of integers $\mathcal{O}_{\mathbf{F}}$ and $\mathfrak{p},\mathfrak{q}$ two squarefree and coprime ideals of $\mathcal{O}_{\mathbf{F}}$, we prove a reciprocity relation for the first moment of the triple product ... More

Rationality of cycles over function fields of $SL_1(A)$-torsorsSep 06 2014In this note we prove a result comparing rationality of algebraic cycles over the function field of a $SL_1(A)$-torsor for a central simple algebra $A$ and over the base field.

Arbitrary threshold widths for monotone symmetric propertiesJan 06 2006We investigate the threshold widths of some symmetric properties which range asymptotically between 1/\sqrt{n} and 1/(log n). These properties are built using a combination of failure sets arising from reliability theory. This combination of sets is simply ... More

Similarity results for operators of class $C_0$ and the algebra $H^\infty(T)$Aug 16 2012May 22 2014Given two multiplicity-free operators $T_1$ and $T_2$ of class $C_0$ having the same finite Blaschke product as minimal function, the operator algebras $H^\infty(T_1)$ and $H^\infty(T_2)$ are isomorphic and $T_1$ is similar to $T_2$. We find conditions ... More

Isolation by distance patterns arising from short range and long range dispersal -- a forwards in time approachJul 18 2019In this paper, we consider a mathematical model for the evolution of neutral genetic diversity in a spatial continuum including mutations, genetic drift and either short range or long range dispersal. The model we consider is the spatial $ \Lambda $-Fleming-Viot ... More

Khovanov-Rozansky homology and 2-braid groupsMar 22 2012Khovanov has given a construction of the Khovanov-Rozansky link invariants (categorifying the HOMFLYPT invariant) using Hochschild cohomology of 2-braid groups. We give a direct proof that his construction does give link invariants. We show more generally ... More

Picard group of the forms of the affine line and of the additive groupOct 07 2016We obtain an explicit upper bound on the torsion of the Picard group of the forms of the affine line and of the additive group, and a sufficient condition for this Picard group to be non trivial. We also give examples of non trivial forms of the affine ... More

Modell zur Entstehung eines Rings aus Dunkler Materie in der MilchstraßenebeneOct 29 2008Jan 15 2010Both the distribution of hydrogen and the rotation curve of the Milky Way indicate the existence of a ring of Cold Dark Matter in the galactic plane with a radius of 14 kiloparsecs around the galactic centre. Using a semianalytical model, the formation ... More

Symmetric correspondences on quadricsNov 14 2016We prove a result comparing the rationality of some elementary algebraic cycles introduced by Alexander Vishik, defined on orthogonal grassmannians, with the rationality of some algebraic cycles defined on fiber products of the corresponding quadric.

Soliton resolution for equivariant wave maps to the sphereMay 23 2013We consider finite energy corotationnal wave maps with target manifold $\m S^2$. We prove that for a sequence of times, they decompose as a sum of decoupled harmonic maps in the light cone, and a smooth wave map (in the blow case) or a linear scattering ... More

On the wonderfulness of Noether's theorems, 100 years later, and Routh reductionApr 05 2018Apr 11 2018This paper is written in honour of the centenary of Emmy Amalie Noether's famous article entitled Invariante Variationsprobleme. It firstly aims to give an exposition of what we believe to be the most significant and elegant issues regarding her theorems, ... More

Symmetric correspondences on quadricsNov 14 2016May 14 2017We prove a result comparing the rationality of some elementary algebraic cycles introduced by Alexander Vishik, defined on orthogonal grassmannians, with the rationality of some algebraic cycles defined on fiber products of the corresponding quadric.

Unperforated pairs of operator spaces and hyperrigidity of operator systemsJun 26 2017Feb 28 2018We study restriction and extension properties for states on C$^*$-algebras with an eye towards hyperrigidity of operator systems. We use these ideas to provide supporting evidence for Arveson's hyperrigidity conjecture. Prompted by various characterizations ... More

A Twisted Fourth Moment of Dirichlet L-functionsNov 29 2016Dec 05 2016We evaluate some twisted fourth moment of Dirichlet $L$-functions at the central point s=1/2 and for prime moduli q. The principal tool is a careful analysis of a shifted convolution problem involving the divisor function using spectral theory of automorphic ... More

$J$-invariant of hermitian forms over quadratic extensionsFeb 12 2016Aug 07 2018We develop the version of the $J$-invariant for hermitian forms over quadratic extensions in a similar way Alexander Vishik did it for quadratic forms. This discrete invariant contains informations about rationality of algebraic cycles on the maximal ... More

The stepping stone model in a random environment and the effect of local heterogneities on isolation by distance patternsJul 06 2018We study a one-dimensional spatial population model where the population sizes at each site are chosen according to a translation invariant and ergodic distribution and are uniformly bounded away from 0 and infinity. We suppose that the frequencies of ... More

Quasisimilarity of invariant subspaces for $C_0$ operators with multiplicity twoSep 17 2011May 22 2014For an operator $T$ of class $C_0$ with multiplicity two, we show that the quasisimilarity class of an invariant subspace $M$ is determined by the quasisimilarity classes of the restriction $T|M$ and of the compression $T_{M^\perp}$. We also provide a ... More

A Twisted Fourth Moment of Dirichlet L-functionsNov 29 2016We evaluate some twisted fourth moment of Dirichlet $L$-functions at the central point s=1/2 and for prime moduli q. The principal tool is a careful analysis of a shifted convolution problem involving the divisor function using spectral theory of automorphic ... More

Non-commutative peaking phenomena and a local version of the hyperrigidity conjectureSep 06 2017Feb 28 2018We investigate various notions of peaking behaviour for states on a $\mathrm{C}^*$-algebra, where the peaking occurs within an operator system. We pay particularly close attention to the existence of sequences of elements forming an approximation of the ... More

On the divergence of Birkhoff Normal FormsJun 03 2019It is well known that a real analytic symplectic diffeomorphism of the two-dimensional annulus admitting a real analytic invariant curve with diophantine rotation number can be {\it formally} conjugated to its Birkhoff Normal Form, a formal power series ... More

An unified approach to the Junta theorem for discrete and continuous modelsFeb 02 2017In a recent paper, T. Austin has proved an analogous theorem for the continuous torus of the original Junta theorem proved by Friedgut in the case of the Boolean cube. Analogous statements have been established recently in discrete cases such as the discrete ... More

Network of Bandits insure Privacy of end-usersFeb 11 2016Mar 29 2017In order to distribute the best arm identification task as close as possible to the user's devices, on the edge of the Radio Access Network, we propose a new problem setting, where distributed players collaborate to find the best arm. This architecture ... More

Fourier analysis methods for the compressible Navier-Stokes equationsJul 09 2015In the last three decades, Fourier analysis methods have known a growing importance in the study of linear and nonlinear PDE's. In particular, techniques based on Littlewood-Paley decomposition and paradifferential calculus have proved to be very efficient ... More

On the well-posedness of the incompressible density-dependent Euler equations in the $L^p$ frameworkJul 23 2009The present paper is devoted to the study of the well-posedness issue for the density-dependent Euler equations in the whole space. We establish local-in-time results for the Cauchy problem pertaining to data in the Besov spaces embedded in the set of ... More

Scaling limit of dynamical percolation on critical Erdös-Rényi random graphsOct 25 2017Jun 22 2018Consider a critical Erd\"os-R\'enyi random graph: $n$ is the number of vertices, each one of the $\binom{n}{2}$ possible edges is kept in the graph independently from the others with probability $n^{-1}+\lambda n^{-4/3}$, $\lambda$ being a fixed real ... More

Similarity results for operators of class C_0Apr 01 2011Oct 05 2011If T is a multiplicity-free contraction of class C_0 with minimal function m_T, then it is quasisimilar to the Jordan block S(m_T). In case m_T is a Blaschke product with simple roots forming a Carleson sequence, we show that the relation between T and ... More

Completely bounded isomorphisms of operator algebras and similarity to complete isometriesJan 03 2014May 22 2014A well-known theorem of Paulsen says that if $\mathcal{A}$ is a unital operator algebra and $\phi:\mathcal{A}\to B(\mathcal{H})$ is a unital completely bounded homomorphism, then $\phi$ is similar to a completely contractive map $\phi'$. Motivated by ... More

Critical control of a genetic algorithmMay 19 2010Based on speculations coming from statistical mechanics and the conjectured existence of critical states, I propose a simple heuristic in order to control the mutation probability and the population size of a genetic algorithm.

Spectral and homological properties of Hilbert modules over the disc algebraJul 19 2013May 22 2014We study general Hilbert modules over the disc algebra and exhibit necessary spectral conditions for the vanishing of certain associated extension groups. In particular, this sheds some light on the problem of identifying the projective Hilbert modules. ... More

Critical population and error threshold on the sharp peak landscape for a Moran modelMay 15 2012Oct 23 2012The goal of this work is to propose a finite population counterpart to Eigen's model, which incorporates stochastic effects. We consider a Moran model describing the evolution of a population of size $m$ of chromosomes of length $\ell$ over an alphabet ... More

$J$-invariant of hermitian formsFeb 12 2016Oct 01 2016We develop the version of the $J$-invariant for hermitian forms in a similar way Alexander Vishik did it for quadratic forms. This discrete invariant contains informations about rationality of algebraic cycles on the maximal unitary grassmannian associated ... More

Network of BanditsFeb 11 2016Oct 11 2016The distribution of machine learning tasks on the user's devices offers several advantages for application purposes: scalability, reduction of deployment costs and privacy. We propose a basic brick, Distributed Median Elimination, which can be used to ... More

Spectral instability of some non-selfadjoint anharmonic oscillatorsJan 22 2013The purpose of this Note is to highlight the spectral instability of some non-selfadjoint differential operators, by studying the growth rate of the norms of the spectral projections $\Pi_n$ associated with their eigenvalues. More precisely, we are concerned ... More

The travel time in a finite box in supercritical Bernoulli percolationJul 11 2013We consider the standard site percolation model on the three dimensional cubic lattice. Starting solely with the hypothesis that $\theta(p)>0$, we prove that, for any $\alpha>0$, there exists $\kappa>0$ such that, with probability larger than $1-1/n^\alpha$, ... More

Non-compact form of the Elementary Discrete InvariantDec 18 2017Sep 05 2018We determine the non-compact form of Vishik's Elementary Discrete Invariant for quadrics. As an application, we obtain new restrictions on the possible values of the Elementary Discrete Invariant by studying the action of Steenrod operations on the algebraic ... More

Picard group of the forms of the affine line and of the additive groupOct 07 2016Nov 21 2016We obtain an explicit upper bound on the torsion of the Picard group of the forms of the affine line and their regular completions. We also obtain a sufficient condition for the Picard group of the forms of the affine line to be non trivial and we give ... More

On the parallel transport in quantum mechanics with an application to three-state systemsMar 11 2019The aim of this article is to give a rigorous although simple treatment of the geometric notions around parallel transport in quantum mechanics. I start by defining the teleparallelism (or generalized Pancharatnam connection) between n-dimensional vector ... More

The stepping stone model in a random environment and the effect of local heterogneities on isolation by distance patternsJul 06 2018Jun 13 2019We study a one-dimensional spatial population model where the population sizes at each site are chosen according to a translation invariant and ergodic distribution and are uniformly bounded away from 0 and infinity. We suppose that the frequencies of ... More

Quasiaffine orbits of invariant subspaces for uniform Jordan operatorsAug 27 2011May 22 2014We consider the problem of classification of invariant subspaces for the class of uniform Jordan operators. We show that given two invariant subspaces $M_1$ and $M_2$ of a uniform Jordan operator $T=S(\theta)\oplus S(\theta)\oplus \ldots$, the subspace ... More

Around rationality of integral cyclesMar 12 2012In this article we prove a result comparing rationality of integral algebraic cycles over the function field of a quadric and over the base field. This is an integral version of the result known for coefficients modulo 2. Those results have already been ... More

On quantitative noise stability and influences for discrete and continuous modelsJan 28 2014Nov 12 2014In [K-K], Keller and Kindler proved a quantitative version of the famous Benjamini - Kalai-Schramm Theorem on noise sensitiviy of Boolean funtions. The result was extented to the continuous Gaussian setting in [K-M-S2] by means of a Central Limit Theorem ... More

Remarks on the lifespan of the solutions to some models of incompressible fluid mechanicsJan 30 2012We give lower bounds for the lifespan of a solution to the inviscid Boussinesq system. In dimension two, we point out that it tends to infinity when the initial (relative) temperature tends to zero. This is, to the best of our knowledge, the first result ... More

A lower bound on the two-arms exponent for critical percolation on the latticeJun 13 2013Oct 29 2015We consider the standard site percolation model on the $d$-dimensional lattice. A direct consequence of the proof of the uniqueness of the infinite cluster of Aizenman, Kesten and Newman [Comm. Math. Phys. 111 (1987) 505-531] is that the two-arms exponent ... More

Parallelizing Stream with FutureMay 19 2013Stream is re-interpreted in terms of a Lazy monad. Future is substituted for Lazy in the obtained construct, resulting in possible parallelization of any algorithm expressible as a Stream computation. The principle is tested against two example algorithms. ... More

Critical population and error threshold on the sharp peak landscape for the Wright-Fisher modelJul 03 2012Jun 19 2015We pursue the task of developing a finite population counterpart to Eigen's model. We consider the classical Wright-Fisher model describing the evolution of a population of size $m$ of chromosomes of length $\ell$ over an alphabet of cardinality $\kappa$. ... More

On the unilateral shift as a Hilbert module over the disc algebraFeb 25 2013May 22 2014We study the unilateral shift (of arbitrary countable multiplicity) as a Hilbert module over the disc algebra and the associated extension groups. In relation with the problem of determining whether this module is projective, we consider a special class ... More

Automizers as extended reflection groupsOct 21 2010Brou\'e, Malle and Michel have shown that the automizer of an abelian Sylow p-subgroup in a finite simple Chevalley group is an irreducible complex reflection group, for p not too small and different from the defining characteristic. The aim is this note ... More

The largest root of random Kac polynomials is heavy tailedApr 10 2017We prove that the largest and smallest root in modulus of random Kac polynomials have a non-universal behavior. They do not converge towards the edge of the support of the limiting distribution of the zeros. This non-universality is surprising as the ... More

The quasispecies regime for the simple genetic algorithm with roulette-wheel selectionJun 30 2015Dec 03 2015We introduce a new parameter to discuss the behavior of a genetic algorithm. This parameter is the mean number of exact copies of the best fit chromosomes from one generation to the next. We argue that the genetic algorithm should operate efficiently ... More

Spectral instability for even non-selfadjoint anharmonic oscillatorsJan 22 2013Oct 17 2013We study the instability of the spectrum for a class of non-selfadjoint anharmonic oscillators, estimating the behavior of the instability indices (i. e. the norm of spectral projections) associated with the large eigenvalues of these oscillators. We ... More

Threshold for monotone symmetric properties through a logarithmic Sobolev inequalityNov 24 2005Nov 20 2006Threshold phenomena are investigated using a general approach, following Talagrand [Ann. Probab. 22 (1994) 1576--1587] and Friedgut and Kalai [Proc. Amer. Math. Soc. 12 (1999) 1017--1054]. The general upper bound for the threshold width of symmetric monotone ... More

Unitary equivalence and similarity to Jordan models for weak contractions of class $C_0$Jun 14 2013May 22 2014We obtain results on the unitary equivalence of weak contractions of class $C_0$ to their Jordan models under an assumption on their commutants. In particular, our work addresses the case of arbitrary finite multiplicity. The main tool is the theory of ... More

The quasispecies regime for the simple genetic algorithm with ranking selectionMar 21 2014We study the simple genetic algorithm with a ranking selection mechanism (linear ranking or tournament). We denote by $\ell$ the length of the chromosomes, by $m$ the population size, by $p_C$ the crossover probability and by $p_M$ the mutation probability. ... More

On the irreducibility of Deligne-Lusztig varietiesJan 16 2006Apr 12 2006Let $G$ be a connected reductive algebraic group defined over an algebraic closure of a finite field and let $F : G \to G$ be an endomorphism such that $F^d$ is a Frobenius endomorphism for some $d \geq 1$. Let $P$ be a parabolic subgroup of $G$ admitting ... More

Convergence of a stochastic particle approximation for fractional scalar conservation lawsJun 21 2010We give a probabilistic numerical method for solving a partial differential equation with fractional diffusion and nonlinear drift. The probabilistic interpretation of this equation uses a system of particles driven by L\'evy alpha-stable processes and ... More

Endoscopie et conjecture raffinée de Gan-Gross-Prasad pour les groupes unitairesDec 05 2012Mar 29 2014Under endoscopic assumptions about $L$-packets of unitary groups, we prove the local Gan-Gross-Prasad conjecture for tempered representations of unitary groups over $p$-adic fields. Roughly, this conjecture says that branching laws for $U(n-1)\subset ... More

Construction of a multi-soliton blow-up solution to the semilinear wave equation in one space dimensionOct 11 2011Apr 24 2012We consider the semilinear wave equation with power nonlinearity in one space dimension. Given a blow-up solution with a characteristic point, we refine the blow-up behavior first derived by Merle and Zaag. We also refine the geometry of the blow-up set ... More

A local trace formula for the Gan-Gross-Prasad conjecture for unitary groups: the archimedean caseJun 04 2015Dec 21 2015In this paper, we prove, following earlier work of Waldspurger ([Wa1], [Wa4]), a sort of local relative trace formula which is related to the local Gan-Gross-Prasad conjecture for unitary groups over a local field $F$ of characteristic zero. As a consequence, ... More

Geometrically-protected reversibility in hydrodynamic Loschmidt-echo experimentsJul 07 2014We demonstrate an archetypal Loschmidt-echo experiment involving thousands of droplets which interact in a reversible fashion via a viscous fluid. Firstly, we show that, unlike equilibrium systems, periodically driven microfluidic emulsions self-organize ... More

Towards an ultra efficient kinetic scheme Part II: The high order caseDec 02 2012In a recent paper we presented a new ultra efficient numerical method for solving kinetic equations of the Boltzmann type (G. Dimarco, R. Loubere, Towards an ultra efficient kinetic scheme. Part I: basics on the 689 BGK equation, J. Comp. Phys., (2013), ... More

Galton-Watson and branching process representations of the normalized Perron-Frobenius eigenvectorMar 23 2018Let $A$ be a primitive matrix and let $\lambda$ be its Perron-Frobenius eigenvalue. We give formulas expressing the associated normalized Perron-Frobenius eigenvector as a simple functional of a multitype Galton-Watson process whose mean matrix is $A$, ... More

A completely bounded non-commutative Choquet boundary for operator spacesMar 08 2017Feb 28 2018We develop a completely bounded counterpart to the non-commutative Choquet boundary of an operator space. We show how the class of completely bounded linear maps is too large to accommodate our purposes. To overcome this obstacle, we isolate the subset ... More

Cancellation of the Anchored isoperimetric profile in bond percolation at p cMar 19 2019We consider the anchored isoperimetric profile of the infinite open cluster, defined for $p > p_c$, whose existence has been recently proved in [3]. We extend adequately the definition for $p = p_c$, in finite boxes. We prove a partial result which implies ... More

There is no isolated interface edge in very supercritical percolationNov 29 2018Jul 03 2019We consider the Bernoulli bond percolation model in a box $\Lambda$ (not necessarily parallel to the directions of the lattice) in the regime where the percolation parameter is close to $1$. We condition the configuration on the event that two opposite ... More

Bicovariograms and Euler characteristic I. Regular setsOct 02 2015Mar 10 2017We establish an expression of the \EC~of a $r$-regular planar set in function of some variographic quantities. The usual $\mathcal{C} ^{2}$ framework is relaxed to a $\mathcal{C} ^{1,1}$ regularity assumption, generalising existing local formulas for ... More

The incompressible limit in $L^p$ type critical spacesSep 25 2014This paper aims at justifying the low Mach number convergence to the incompressible Navier-Stokes equations for viscous compressible flows in the ill-prepared data case. The fluid domain is either the whole space, or the torus. A number of works have ... More

Lower large deviations for the maximal flow through a domain of $\mathbb{R}^d$ in first passage percolationJul 31 2009We consider the standard first passage percolation model in the rescaled graph $\mathbb{Z}^d/n$ for $d\geq 2$, and a domain $\Omega$ of boundary $\Gamma$ in $\mathbb{R}^d$. Let $\Gamma^1$ and $\Gamma^2$ be two disjoint open subsets of $\Gamma$, representing ... More

Weak shape theorem in first passage percolation with infinite passage timesApr 17 2014Nov 20 2014We consider the model of i.i.d. first passage percolation on $\mathbb{Z}^d$ : we associate with each edge $e$ of the graph a passage time $t(e)$ taking values in $[0,+\infty]$, such that $\mathbb{P}[t(e)<+\infty] >p_c(d)$. Equivalently, we consider a ... More

Multiplier algebras of complete Nevanlinna-Pick spaces: dilations, boundary representations and hyperrigidityDec 12 2016Oct 20 2017We study reproducing kernel Hilbert spaces on the unit ball with the complete Nevanlinna-Pick property through the representation theory of their algebras of multipliers. We give a complete description of the representations in terms of the reproducing ... More

The distribution of the quasispecies for a Moran model on the sharp peak landscapeDec 10 2013We consider the Moran model on the sharp peak landscape, in the asymptotic regime studied in [3], where a quasispecies is formed. We find explicitly the distribution of this quasispecies.

Intermittency in spherical Couette dynamosApr 23 2013We investigate dynamo action in three-dimensional numerical simulations of turbulent spherical Couette flows. Close to the onset of dynamo action, the magnetic field exhibits an intermittent behavior, characterized by a series of short bursts of the magnetic ... More

Nanomechanics of single keratin fibres: A Raman study of the alpha helix -> beta sheet transition and water effectJun 06 2007The use of micro-Raman spectroscopy, through chemical bond nano-scale probes, allows the changes in conformations (alpha helix -> beta sheet), chain orientation, disconnection of disulfide bonds (-20%) and the increase of intra and inter-chain distances ... More

Monotonic cocyclesOct 02 2013We develop a "local theory" of multidimensional quasiperiodic $\SL(2,\R)$ cocycles which are not homotopic to a constant. It describes a $C^1$-open neighborhood of cocycles of rotations and applies irrespective of arithmetic conditions on the frequency, ... More

Archimedean theory and $ε$-factors for the Asai Rankin-Selberg integralsNov 30 2018In this paper, we partially complete the local Rankin-Selberg theory of Asai $L$-functions and $\epsilon$-factors as introduced by Flicker and Kable. In particular, we establish the relevant local functional equation at Archimedean places and prove the ... More

A new proof of Jacquet-Rallis's fundamental lemmaJan 09 2019We give a new proof of the so-called Lie algebra version of Jacquet-Rallis's fundamental lemma for local non-Archimedean fields of characteristic zero. This proof is local and based on previous results of W. Zhang on the existence of a certain smooth ... More

Joint similarity for commuting families of power bounded matricesJun 23 2018An example due to Pisier shows that two commuting, completely polynomially bounded Hilbert space operators may not be simultaneously similar to contractions. Thus, while each operator is individually similar to a contraction, the pair is not jointly similar ... More

A new look at the interfaces in percolationJun 22 2018Jun 21 2019We propose a new definition of the interface in the context of the Bernoulli percolation model. We construct a coupling between two percolation configurations, one which is a standard percolation configuration, and one which is a percolation configuration ... More

On small travelling waves to the mass critical fractional NLSDec 12 2017We consider the mass critical fractional (NLS). We show the existence of travelling waves for all mass below the ground state mass, and give a complete description of the associated profiles in the small mass limit. We therefore recover a situation similar ... More

Universal large deviations for Kac polynomialsJul 08 2016We prove the universality of the large deviations principle for the empirical measures of zeros of random polynomials whose coefficients are i.i.d. random variables possessing a density with respect to the Lebesgue measure on C, R or R + , under the assumption ... More

Optimal time-decay estimates for the compressible navier-stokes equations in the critical l p frameworkMay 03 2016The global existence issue for the isentropic compressible Navier-Stokes equations in the critical regularity framework has been addressed in [7] more than fifteen years ago. However, whether (optimal) time-decay rates could be shown in general critical ... More

Bicovariograms and Euler characteristic of random fields excursionsOct 02 2015Dec 07 2018Let f be a C1 bivariate function with Lipschitz derivatives, and F = {x $\in$ R2 : f(x) $\lambda$} an upper level set of f, with $\lambda$ $\in$ R. We present a new identity giving the Euler characteristic of F in terms of its three-points indicator functions. ... More

Comparison of local spherical characters and the Ichino-Ikeda conjecture for unitary groupsFeb 21 2016Sep 22 2017In this paper, we prove a conjecture of Wei Zhang on comparison of certain local spherical characters from which we draw some consequences for the Ichino-Ikeda conjecture for unitary groups.

On the well-posedness of the full compressible Navier-Stokes system in critical Besov spacesJul 17 2014We are concerned with the Cauchy problem of the full compressible Navier-Stokes equations satisfied by viscous and heat conducting fluids in $\mathbb{R}^n.$ We focus on the so-called critical Besov regularity framework. In this setting, it is natural ... More

Topological quantization by controlled paths: application to Cooper pairs pumpsNov 05 2007When physical systems are tunable by three classical parameters, level degeneracies may occur at isolated points in parameter space. A topological singularity in the phase of the degenerate eigenvectors exists at these points. When a path encloses such ... More

A new look at the interfaces in percolationJun 22 2018We propose a new definition of the interface in the context of the Bernoulli percolation model. We construct a coupling between two percolation configurations, one which is a standard percolation configuration, and one which is a percolation configuration ... More

Mixing HOL and Coq in Dedukti (Extended Abstract)Jul 31 2015We use Dedukti as a logical framework for interoperability. We use automated tools to translate different developments made in HOL and in Coq to Dedukti, and we combine them to prove new results. We illustrate our approach with a concrete example where ... More

The Oberbeck-Boussinesq approximation in critical spacesApr 16 2013In this paper we study the validity of the so-called Oberbeck-Boussinesq approximation for compressible viscous perfect gases in the whole three-dimensional space. Both the cases of uids with positive heat conductivity and zero conductivity are considered. ... More

Upper large deviations for the maximal flow through a domain of $\bolds{\mathbb{R}^d}$ in first passage percolationJul 31 2009Feb 17 2012We consider the standard first passage percolation model in the rescaled graph $\mathbb {Z}^d/n$ for $d\geq2$ and a domain $\Omega$ of boundary $\Gamma$ in $\mathbb {R}^d$. Let $\Gamma ^1$ and $\Gamma ^2$ be two disjoint open subsets of $\Gamma$ representing ... More

Lower large deviations for the maximal flow through tilted cylinders in two-dimensional first passage percolationDec 18 2009Equip the edges of the lattice $\mathbb{Z}^2$ with i.i.d. random capacities. A law of large numbers is known for the maximal flow crossing a rectangle in $\mathbb{R}^2$ when the side lengths of the rectangle go to infinity. We prove that the lower large ... More

Lower large deviations and laws of large numbers for maximal flows through a box in first passage percolationJan 07 2008Jul 03 2009We consider the standard first passage percolation model in $\mathbb{Z}^d$ for $d\geq 2$. We are interested in two quantities, the maximal flow $\tau$ between the lower half and the upper half of the box, and the maximal flow $\phi$ between the top and ... More

A Lower Bound on the Relative Entropy with Respect to a Symmetric ProbabilityJul 03 2014Oct 20 2014Let $\rho$ and $\mu$ be two probability measures on $\mathbb{R}$ which are not the Dirac mass at $0$. We denote by $H(\mu|\rho)$ the relative entropy of $\mu$ with respect to $\rho$. We prove that, if $\rho$ is symmetric and $\mu$ has a finite first moment, ... More

A central limit theorem for the spatial Lambda Fleming-Viot process with selectionDec 18 2015Mar 09 2016We study the evolution of gene frequencies in a population living in $\mathbb{R}^d$, modelled by the spatial Lambda Fleming-Viot process with natural selection (Barton, Etheridge and Veber, 2010 and Etheridge, Veber and Yu, 2014). We suppose that the ... More

Integrability of $\mathcal W({\mathfrak{sl}_d})$-symmetric Toda conformal field theories I : Quantum geometryJan 10 2018Jan 23 2019In this article which is the first of a series of three, we consider $\mathcal W({\mathfrak{sl}_d})$-symmetric conformal field theory in topological regimes for a generic value of the background charge, where $\mathcal W({\mathfrak{sl}_d})$ is the W-algebra ... More