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Simple closed geodesics and the study of Teichmüller spacesDec 08 2009The goal of the chapter is to present certain aspects of the relationship between the study of simple closed geodesics and Teichm\"uller spaces.

Quillen-Segal algebras and Stable homotopy theoryJul 27 2018Let $\mathscr{M}$ be a monoidal model category that is also combinatorial and left proper. If $\mathscr{O}$ is a monad, operad, properad, or a PROP; following Segal's ideas we develop a theory of Quillen-Segal $\mathscr{O}$-algebras and show that we have ... More

Optimal DVB-S2 spectral efficiency with hierarchical modulationNov 19 2014We study the design of a DVB-S2 system in order to maximise spectral efficiency. This task is usually challenging due to channel variability. The solution adopted in modern satellite communications systems such as DVB-SH and DVB-S2 relies mainly on a ... More

Setting new Cosmology constraints with ALMAMar 06 2014Mar 17 2014I make a short revision of Cosmology questions which ALMA was built to address. Without diving into much detail, I point out the ALMA specifications and strategies which are expected to provide a better handle of: the temperature evolution of the Cosmic ... More

Glass and jamming transition of simple liquids: static and dynamic theoryJul 15 2013We study the glass and jamming transition of finite-dimensional models of simple liquids: hard- spheres, harmonic spheres and more generally bounded pair potentials that modelize frictionless spheres in interaction. At finite temperature, we study their ... More

Quantitative quenched Voronoi percolation and applicationsJun 21 2018Sep 28 2018In [AGMT16], Ahlberg, Griffiths, Morris and Tassion prove that, asymptotically almost surely, the quenched crossing probabilities for critical planar Voronoi percolation do not depend on the environment. We prove an analogous result for arm events; in ... More

Effective Approaches to QCDApr 11 2018In this lecture I will explain the established pictures of the QCD vacuum and, in particular, the underlying confinement mechanism. These are: the magnetic monopole condensation (dual Mei\ss ner effect), the center vortex picture and the Gribov--Zwanziger ... More

Asymptotic equivalence of probability measures and stochastic processesAug 09 2017Jan 30 2018Let $P_n$ and $Q_n$ be two probability measures representing two different probabilistic models of some system (e.g., an $n$-particle equilibrium system, a set of random graphs with $n$ vertices, or a stochastic process evolving over a time $n$) and let ... More

Introduction to dynamical large deviations of Markov processesMay 18 2017Nov 03 2017These notes give a summary of techniques used in large deviation theory to study the fluctuations of time-additive quantities, called dynamical observables, defined in the context of Langevin-type equations, which model equilibrium and nonequilibrium ... More

The Wilson loop in light-front quantizationDec 22 2016Using Dirac's method for the quantization of constrained systems QED is canonically quantized in the front-form in a gauge which is the light-front analog of the Weyl gauge. From the obtained vacuum wave functional the spatial Wilson loop is calculated. ... More

Interrogating surface length spectra and quantifying isospectralityNov 07 2016This article is about inverse spectral problems for hyperbolic surfaces and in particular how length spectra relate to the geometry of the underlying surface. A quantitative answer is given to the following: how many questions do you need to ask a length ... More

Central Limit Theorem and Large Deviation Principle for Continuous Time Open Quantum WalksOct 05 2016Jun 20 2017Open Quantum Walks (OQWs), originally introduced by S. Attal, are quantum generalizations of classical Markov chains. Recently, natural continuous time models of OQW have been developed by C. Pellegrini. These models, called Continuous Time Open Quantum ... More

$GL_2$-real analytic Eisenstein series twisted by parameter matrices and multiplicative integral quasi-charactersJul 11 2016In this monograph, we study in detail a special class of $GL_2$-real analytic Eisenstein series.

Scaled penalization of Brownian motion with drift and the Brownian ascentMar 12 2018May 29 2018We study a scaled version of a two-parameter Brownian penalization model introduced by Roynette-Vallois-Yor in arXiv:math/0511102. The original model penalizes Brownian motion with drift $h\in\mathbb{R}$ by the weight process ${\big(\exp(\nu S_t):t\geq ... More

A Note on the Forward-Douglas--Rachford Splitting for Monotone Inclusion and Convex OptimizationApr 23 2017Apr 27 2018We shed light on the structure of the "three-operator" version of the forward-Douglas--Rachford splitting algorithm for finding a zero of a sum of maximally monotone operators $A + B + C$, where $B$ is cocoercive, involving only the computation of $B$ ... More

The large deviation approach to statistical mechanicsApr 02 2008Aug 20 2009The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield ... More

A Class of Zielonka Automata with a Decidable Controller Synthesis ProblemJan 20 2016Feb 02 2016The decidability of the distributed version of the Ramadge and Wonham control problem (Ramadge and Wonham 1989), where both the plant and the controllers are modelled as Zielonka au-tomata (Zielonka 1987; Diekert and Rozenberg 1995) is a challenging open ... More

Hamiltonian finite-temperature quantum field theory from its vacuum on partially compactified spaceApr 21 2016The partition function of a relativistic invariant quantum field theory is expressed by its vacuum energy calculated on a spatial manifold with one dimension compactified to a 1-sphere $S^1 (\beta)$, whose circumference $\beta$ represents the inverse ... More

Computing Jacobi's $θ$ in quasi-linear timeNov 13 2015Jacobi's $\theta$ function has numerous applications in mathematics and computer science; a naive algorithm allows the computation of $\theta(z,\tau)$, for $z, \tau$ verifying certain conditions, with precision $P$ in $O(\mathcal{M}(P) \sqrt{P})$ bit ... More

Phenomenology of extra quarks at the LHCJul 13 2018We study in a model independent way models of new Physics featuring extra quarks (XQs). These XQs are predicted by extensions of the Standard Model (SM) but have never been observed yet even though many searches have been designed to find them at the ... More

Comment on "Towards a large deviation theory for strongly correlated systems"Sep 12 2012Jan 14 2013I comment on a recent paper by Ruiz and Tsallis [Phys. Lett. A 376, 2451 (2012)] claiming to have found a '$q$-exponential' generalization of the large deviation principle for strongly correlated random variables. I show that the basic scaling results ... More

Relationships between p-unit constructions for real quadratic fieldsApr 10 2010Let $K$ be a real quadratic field and let $p$ be a prime number which is inert in $K$. Let $K_p$ be the completion of $K$ at $p$. In a previous paper, we constructed a $p$-adic invariant $u_C\in K_p$, and we proved a $p$-adic Kronecker limit formula relating ... More

Genetic cellular neural networks for generating three-dimensional geometryMar 28 2016There are a number of ways to procedurally generate interesting three-dimensional shapes, and a method where a cellular neural network is combined with a mesh growth algorithm is presented here. The aim is to create a shape from a genetic code in such ... More

A basic introduction to large deviations: Theory, applications, simulationsJun 21 2011Feb 29 2012The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic system is observed, ... More

Simple spin models with non-concave entropiesApr 01 2005Jan 24 2008Two simple spin models are studied to show that the microcanonical entropy can be a non-concave function of the energy, and that the microcanonical and canonical ensembles can give non-equivalent descriptions of the same system in the thermodynamic limit. ... More

Kissing numbers for surfacesNov 15 2011The so-called {\it kissing number} for hyperbolic surfaces is the maximum number of homotopically distinct systoles a surface of given genus $g$ can have. These numbers, first studied (and named) by Schmutz Schaller by analogy with lattice sphere packings, ... More

A multiwavelength study of near- and mid-infrared selected galaxies at high redshift: ERGs, AGN-identification and the contribution from dustOct 12 2011Nov 17 2011The main focus of this thesis is the IR spectral regime, which since the 70's and 80's has revolutionised our understanding of the Universe. A multi-wavelength analysis on Extremely Red Galaxy populations is first presented in one of the most intensively ... More

Time-convexity of the entropy in the multiphasic formulation of the incompressible euler equationJan 23 2017Sep 06 2017We study the multiphasic formulation of the incompressible Euler equation introduced by Brenier: infinitely many phases evolve according to the compressible Euler equation and are coupled through a global in-compressibility constraint. We are able to ... More

On the Control of Asynchronous AutomataJan 20 2016Aug 04 2017The decidability of the distributed version of the Ramadge and Wonham controller synthesis problem,where both the plant and the controllers are modeled as asynchronous automataand the controllers have causal memoryis a challenging open problem.There exist ... More

Approaching the Gaussian channel capacity with APSK constellationsMar 16 2015We consider the Gaussian channel with power constraint P. A gap exists between the channel capacity and the highest achievable rate of equiprobable uniformly spaced signal. Several approaches enable to overcome this limitation such as constellations with ... More

The homology systole of hyperbolic Riemann surfacesOct 02 2010Apr 07 2011The main goal of this note is to show that the study of closed hyperbolic surfaces with maximum length systole is in fact the study of surfaces with maximum length homological systole. The same result is shown to be true for once-punctured surfaces, and ... More

Repeated Binomial Coefficients and High-Degree CurvesNov 15 2014We consider the problem of characterizing solutions in $(x, y)$ to the equation ${x \choose y}={{x-a} \choose {y+b}}$ in terms of $a$ and $b$. We obtain one simple result which allows the determination of a ratio in terms of $a$ and $b$ which the ratio ... More

Methods for calculating nonconcave entropiesMar 01 2010Apr 28 2010Five different methods which can be used to analytically calculate entropies that are nonconcave as functions of the energy in the thermodynamic limit are discussed and compared. The five methods are based on the following ideas and techniques: i) microcanonical ... More

Comment on "First-order phase transitions: equivalence between bimodalities and the Yang-Lee theorem"Mar 02 2005I discuss the validity of a result put forward recently by Chomaz and Gulminelli [Physica A 330 (2003) 451] concerning the equivalence of two definitions of first-order phase transitions. I show that distributions of zeros of the partition function fulfilling ... More

Numerical Simulations of Galactic Outflows and Evolution of the IGMOct 05 2011Galactic outflows play a major role in the evolution of galaxies and the intergalactic medium (IGM). The energy deposited into the interstellar medium by supernovae and active galactic nuclei can accelerate the gas past the escape velocity, and eject ... More

On the controller synthesis problem for distributed systems with causal memoryJan 20 2016Oct 25 2016The decidability of the distributed version of the Ramadge and Wonham controller synthesis problemwhere both the plant and the controllers are modelled as Zielonka automataand the controllers have causal memoryis a challenging open problem.There exists ... More

Generation of Gaussian Density FieldsJun 22 2005Jul 15 2005This document describes analytical and numerical techniques for the generation of Gaussian density fields, which represent cosmological density perturbations. The mathematical techniques involved in the generation of density harmonics in k-space, the ... More

Annealed scaling relations for Voronoi percolationJun 21 2018Sep 28 2018We prove annealed scaling relations for planar Voronoi percolation. To our knowledge, this is the first result of this kind for a continuum percolation model. We are mostly inspired by the proof of scaling relations for Bernoulli percolation by Kesten ... More

Quantitative predictions from competition theory with incomplete information on model parameters tested against experiments across diverse taxaAug 11 2017We derive an analytical approximation for making quantitative predictions for ecological communities as a function of the mean intensity of the inter-specific competition and the species richness. This method, with only a fraction of the model parameters ... More

Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levelsMar 26 2014Feb 13 2015We present general and rigorous results showing that the microcanonical and canonical ensembles are equivalent at all three levels of description considered in statistical mechanics - namely, thermodynamics, equilibrium macrostates, and microstate measures ... More

The Monadic Second Order Theory of Grid-Free 1-Safe Petri Nets is DecidableFeb 09 2018Feb 16 2018Finite 1-safe Petri nets, also called \emph{net systems}, are natural models of asynchronous concurrency. The event structure of a net system describes all its possible executions and their concurrent nature: two events may be causally ordered, occur ... More

A short note on short pantsApr 28 2013May 22 2013It is a theorem of Bers that any closed hyperbolic surface admits a pants decomposition consisting of curves of bounded length where the bound only depends on the topology of the surface. The question of the quantification of the optimal constants has ... More

Fixed point free involutions on Riemann surfacesApr 06 2005Jul 09 2005Involutions without fixed points on hyperbolic closed Riemann surface are discussed. For an orientable surface $X$ of even genus with an arbitrary Riemannian metric $d$ admitting an involution $\tau$, it is known that $\min_{p\in X}d(p,\tau(p))$ is bounded ... More

Localising Relational Degrees of Freedom in Quantum MechanicsFeb 13 2006This thesis presents a wide-ranging study of localising relational degrees of freedom. Three physical systems are studied in depth, each built upon a simple measurement-based process. For each physical system - light from independent sources leaking onto ... More

Central Limit Theorem and Large Deviation Principle for Continuous Time Open Quantum WalksOct 05 2016Open Quantum Walks (OQWs), originally introduced by S. Attal, are quantum generalizations of classical Markov chains. Recently, natural continuous time models of OQW have been developed by C. Pellegrini. These models, called Continuous Time Open Quantum ... More

Topological contributions to fermionic correlators and nonperturbative aspects of QCD in two dimensionsJun 27 1998We analyze the formation of fermionic condensates in two dimensional quantum chromodynamics for matter in the fundamental representation of the gauge group. We show that a topological regular instanton background is crucial in order to obtain nontrivial ... More

Ensemble equivalence for general many-body systemsJun 15 2011Nov 15 2011It has been proved for a class of mean-field and long-range systems that the concavity of the thermodynamic entropy determines whether the microcanonical and canonical ensembles are equivalent at the level of their equilibrium states, i.e., whether they ... More

Temperature fluctuations and mixtures of equilibrium states in the canonical ensembleDec 12 2002Dec 12 2002It has been suggested recently that `$q$-exponential' distributions which form the basis of Tsallis' non-extensive thermostatistical formalism may be viewed as mixtures of exponential (Gibbs) distributions characterized by a fluctuating inverse temperature. ... More

When is a quantity additive, and when is it extensive?Jan 09 2002The difference between the terms additivity and extensivity, as well as their respective negations, is critically analyzed and illustrated with a few examples. The concepts of subadditivity, pseudo-additivity, and pseudo-extensivity are also defined.

Comment on "Entropy Generation in Computation and the Second law of Thermodynamics", by S. Ishioka and N. FuchikamiFeb 19 1999This brief note argues that, contrary to the claim of Ishioka and Fuchikami (chao-dyn/9902012), Landauer's principle is concerned a priori with entropy generation in computing processes. The concept of heat, in this principle, is only relevant when a ... More

Annealed scaling relations for Voronoi percolationJun 21 2018Apr 30 2019We prove annealed scaling relations for planar Voronoi percolation. To our knowledge, this is the first result of this kind for a continuum percolation model. We are mostly inspired by the proof of scaling relations for Bernoulli percolation by Kesten ... More

Harmonic mappings valued in the Wasserstein spaceDec 20 2017We propose a definition of the Dirichlet energy (which is roughly speaking the integral of the square of the gradient) for mappings mu : Omega -> (P(D), W\_2) defined over a subset Omega of R^p and valued in the space P(D) of probability measures on a ... More

Blackwell-Optimal Strategies in Priority Mean-Payoff GamesJun 08 2010We examine perfect information stochastic mean-payoff games - a class of games containing as special sub-classes the usual mean-payoff games and parity games. We show that deterministic memoryless strategies that are optimal for discounted games with ... More

Anomalous structural evolution of soft particles: Equibrium liquid state theoryDec 14 2009We use the hyper-netted chain approximation of liquid state theory to analyze the evolution with density of the pair correlation function in a model of soft spheres with harmonic repulsion. As observed in recent experiments on jammed soft particles, theory ... More

Optical homodyne tomography with polynomial series expansionJul 04 2011Nov 11 2011We present and demonstrate a method for optical homodyne tomography based on the inverse Radon transform. Different from the usual filtered back-projection algorithm, this method uses an appropriate polynomial series to expand the Wigner function and ... More

The Coulomb gauge ghost Dyson-Schwinger equationJul 15 2010Nov 21 2010A numerical study of the ghost Dyson-Schwinger equation in Coulomb gauge is performed and solutions for the ghost propagator found. As input, lattice results for the spatial gluon propagator are used. It is shown that in order to solve completely, the ... More

Solving Simple Stochastic Games with Few Random VerticesDec 11 2007May 25 2009Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them rely on the existence ... More

Generalized Random Phase Approximation and Gauge TheoriesJun 24 2003Mean-field treatments of Yang-Mills theory face the problem of how to treat the Gauss law constraint. In this paper we try to face this problem by studying the excited states instead of the ground state. For this purpose we extend the operator approach ... More

Conference ImpressionDec 22 1999This paper gives a personal impression of the conference ``Asymmetrical PNe II: From Origins to Microstructures'', flags some of the highlights, gathers together some facts and terminology, and indicates some promising future lines of work in this field. ... More

Effective potential for the order parameter of the SU(2) Yang-Mills deconfinement transitionSep 16 1997The Polyakov loop variable serves as an order parameter to characterize the confined and deconfined phases of Yang-Mills theory. By integrating out the vector fields in the SU(2) Yang-Mills partition function in one-loop approximation, an effective action ... More

Monopoles contra vortices in SU(2) lattice gauge theory?Mar 18 1997We show that the scenario of vortex induced confinement of center--projected SU(2) lattice gauge theory is not necessarily in conflict with the findings in the positive plaquette model.

Exceptional times for percolation under exclusion dynamicsMay 16 2016May 27 2016We analyse in this paper a conservative analogue of the celebrated model of dynamical percolation introduced by H\"aggstr\"om, Peres and Steif in [HPS97]. It is simply defined as follows: start with an initial percolation configuration $\omega(t=0)$. ... More

Comment on "Some non-conventional ideas about algorithmic complexity"Mar 16 2005We comment on a recent paper by D'Abramo [Chaos, Solitons & Fractals, 25 (2005) 29], focusing on the author's statement that an algorithm can produce a list of strings containing at least one string whose algorithmic complexity is greater than that of ... More

Nonconcave entropies in multifractals and the thermodynamic formalismJul 15 2005Dec 04 2006We discuss a subtlety involved in the calculation of multifractal spectra when these are expressed as Legendre-Fenchel transforms of functions analogous to free energy functions. We show that the Legendre-Fenchel transform of a free energy function yields ... More

3D Polyominoes inscribed in a rectangular prismSep 24 2010We introduce a family of 3D combinatorial objects that we define as minimal 3D polyominoes inscribed in a rectanglar prism. These objects are connected sets of unitary cubic cells inscribed in a given rectangular prism and of minimal volume under this ... More

Disambiguating the role of noise correlations when decoding neural populations togetherAug 19 2016Objective: Integrating information from populations of correlated neurons can become too complex even for the human brain. Ignoring correlations may simplify the process but also cause an information loss. This loss has been quantified using many methods, ... More

What are single photons good for?Feb 02 2012In a long-held preconception, photons play a central role in present-day quantum technologies. But what are sources producing photons one by one good for precisely? Well, in opposition to what many suggest, we show that single-photon sources are not helpful ... More

Catastrophic Phase Transitions and Early Warnings in a Spatial Ecological ModelOct 06 2009Gradual changes in exploitation, nutrient loading, etc. produce shifts between alternative stable states (ASS) in ecosystems which, quite often, are not smooth but abrupt or catastrophic. Early warnings of such catastrophic regime shifts are fundamental ... More

Information-Theoretic Limits of ControlMay 26 1999Fundamental limits on the controllability of physical systems are discussed in the light of information theory. It is shown that the second law of thermodynamics, when generalized to include information, sets absolute limits to the minimum amount of dissipation ... More

Generating Paths with WFCAug 13 2018Motion plans are often randomly generated for minor game NPCs. Repetitive or regular movements, however, require non-trivial programming effort and/or integration with a pathing system. We here describe an example-based approach to path generation that ... More

New estimates on the regularity of the pressure in density-constrained Mean Field GamesNov 22 2018We consider variational Mean Field Games endowed with a constraint on the maximal density of the distribution of players. Minimizers of the variational formulation are equilibria for a game where both the running cost and the final cost of each player ... More

Ground States for a nonlinear Schrödinger system with sublinear coupling termsApr 17 2015We study the existence of ground states for the coupled Schr\"odinger system \begin{equation} \left\{\begin{array}{lll} \displaystyle -\Delta u_i+\lambda_i u_i= \mu_i |u_i|^{2q-2}u_i+\sum_{j\neq i}b_{ij} |u_j|^q|u_i|^{q-2}u_i \\ u_i\in H^1(\mathbb{R}^n), ... More

ProvGen: generating synthetic PROV graphs with predictable structureJun 10 2014This paper introduces provGen, a generator aimed at producing large synthetic provenance graphs with predictable properties and of arbitrary size. Synthetic provenance graphs serve two main purposes. Firstly, they provide a variety of controlled workloads ... More

Renormalized vacuum polarization of rotating black holesFeb 04 2015May 05 2015Quantum field theory on rotating black hole spacetimes is plagued with technical difficulties. Here, we describe a general method to renormalize and compute the vacuum polarization of a quantum field in the Hartle-Hawking state on rotating black holes. ... More

Two-Player Perfect-Information Shift-Invariant Submixing Stochastic Games Are Half-PositionalJan 25 2014Oct 08 2015We consider zero-sum stochastic games with perfect information and finitely many states and actions. The payoff is computed by a payoff function which associates to each infinite sequence of states and actions a real number. We prove that if the the payoff ... More

Quark gap equation in an external magnetic fieldOct 22 2013The nonperturbative quark gap equation under the rainbow truncation and with two versions of a phenomenological one-gluon exchange interaction is studied in the presence of a uniform external magnetic field, with emphasis on the small field limit. The ... More

Toward a strictification theorem for co-Segal categoriesJul 27 2013Aug 01 2013We show that for a monoidal model category $\M=(\ul{M}, \otimes, I)$, certain co-Segal $\M$-categories are equivalent to strict ones.

The Diagonalized Newton Algorithm for Nonnegative Matrix FactorizationJan 15 2013Mar 18 2013Non-negative matrix factorization (NMF) has become a popular machine learning approach to many problems in text mining, speech and image processing, bio-informatics and seismic data analysis to name a few. In NMF, a matrix of non-negative data is approximated ... More

On the singular p-Laplacian system under Navier slip type boundary conditions. The gradient-symmetric caseDec 24 2012We consider the p-Laplacian system of N equations in n space variables, 1< p\leq 2, under the homogeneous Navier slip boundary condition. Furthermore, the gradient of the velocity is replaced by the, more physical, symmetric gradient. We prove W^{2, q} ... More

Divergence of the correlation length for critical planar FK percolation with $1\le q\le4$ via parafermionic observablesAug 18 2012Sep 23 2012Parafermionic observables were introduced by Smirnov for planar FK percolation in order to study the critical phase $(p,q)=(p_c(q),q)$. This article gathers several known properties of these observables. Some of these properties are used to prove the ... More

Teaching introductory STEM with the Marble GameOct 12 2012Oct 22 2012Recently there have been multiple calls for curricular reforms to develop new pathways to the science, technology, engineering and math (STEM) disciplines. The Marble Game answers these calls by providing a conceptual framework for quantitative scientific ... More

Quantifying the sparseness of simple geodesics on hyperbolic surfacesJun 04 2018The goal of the article is to provide different explicit quantifications of the non density of simple closed geodesics on hyperbolic surfaces. In particular, we show that within any embedded metric disk on a surface, lies a disk of radius only depending ... More

Target and Conditional Sensitivity Analysis with Emphasis on Dependence MeasuresJan 29 2018Mar 30 2018In the context of sensitivity analysis of complex phenomena in presence of uncertainty, we motivate and precise the idea of orienting the analysis towards a critical domain of the studied phenomenon. We make a brief history of related approaches in the ... More

Sixty years of percolationDec 13 2017Percolation models describe the inside of a porous material. The theory emerged timidly in the middle of the twentieth century before becoming one of the major objects of interest in probability and mathematical physics. The golden age of percolation ... More

Lectures on the Ising and Potts models on the hypercubic latticeJul 03 2017Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids (lattice gases). ... More

Covariant variational approach to Yang-Mills Theory: ThermodynamicsMay 15 2017Jun 30 2017The thermodynamics of $SU(2)$ Yang-Mills theory in the covariant variational approach is studied by relating the free action density in the background of a non-trivial Polyakov loop to the pressure of the gluon plasma. The correct subtraction of the vacuum ... More

Towards computable analysis on the generalised real lineApr 10 2017In this paper we use infinitary Turing machines with tapes of length $\kappa$ and which run for time $\kappa$ as presented, e.g., by Koepke \& Seyfferth, to generalise the notion of type two computability to $2^{\kappa}$, where $\kappa$ is an uncountable ... More

Quantum-enhanced multi-parameter estimation for unitary photonic systemsDec 12 2016Jun 19 2017Precise device characterization is a fundamental requirement for a large range of applications using photonic hardware, and constitutes a multi-parameter estimation problem. Estimates based on measurements using single photons or classical light have ... More

Pure and Stationary Optimal Strategies in Perfect-Information Stochastic Games with Global PreferencesNov 25 2016We examine the problem of the existence of optimal deterministic stationary strategiesintwo-players antagonistic (zero-sum) perfect information stochastic games with finitely many states and actions.We show that the existenceof such strategies follows ... More

Violation of the PT-symmetry and structure formation in the dark matter-gravitational wave interactionSep 07 2016In flat spacetime, quantum fluctuations in dark matter, as described as a Bose-Einstein condensate, are stable and display a relativistic Bogoliubov dispersion relation. In the weak gravitational field limit, both relativistic and nonrelativistic models ... More

Random currents expansion of the Ising modelJul 23 2016Jul 14 2017Critical behavior at an order/disorder phase transition has been a central object of interest in statistical physics. In the past century, techniques borrowed from many different fields of mathematics (Algebra, Combinatorics, Probability, Complex Analysis, ... More

Uniform spaces and the Newtonian structure of (big)data affinity kernelsJan 13 2017Let $X$ be a (data) set. Let $K(x,y)>0$ be a measure of the affinity between the data points $x$ and $y$. We prove that $K$ has the structure of a Newtonian potential $K(x,y)=\varphi(d(x,y))$ with $\varphi$ decreasing and $d$ a quasi-metric on $X$ under ... More

Minimal length of two intersecting simple closed geodesicsAug 02 2006Aug 14 2006On a hyperbolic Riemann surface, given two simple closed geodesics that intersect $n$ times, we address the question of a sharp lower bound $L_n$ on the length attained by the longest of the two geodesics. We show the existence of a surface $S_n$ on which ... More

The critical threshold for Bargmann-Fock percolationNov 14 2017Dec 20 2017In this article, we study the excursions sets $\mathcal{D}\_p=f^{-1}([-p,+\infty[)$ where $f$ is a natural real-analytic planar Gaussian field called the Bargmann-Fock field. More precisely, $f$ is the centered Gaussian field on $\mathbb{R}^2$ with covariance ... More

Quasi-independence for nodal linesNov 14 2017Apr 30 2019We prove a quasi-independence result for level sets of a planar centered stationary Gaussian field with covariance $(x,y)\mapsto\kappa(x-y)$. As a first application, we study percolation for nodal lines in the spirit of [BG16]. In the said article, Beffara ... More

Least energy nodal solutions of Hamiltonian elliptic systems with Neumann boundary conditionsJun 26 2017May 02 2018We study existence, regularity, and qualitative properties of solutions to the system \[ -\Delta u = |v|^{q-1} v\quad \text{ in }\Omega,\qquad -\Delta v = |u|^{p-1} u\quad \text{ in }\Omega,\qquad \partial_\nu u=\partial_\nu v=0\quad \text{ on }\partial\Omega, ... More

Systoles and kissing numbers of finite area hyperbolic surfacesAug 26 2014Sep 29 2015We study the number and the length of systoles on complete finite area orientable hyperbolic surfaces. In particular, we prove upper bounds on the number of systoles that a surface can have (the so-called kissing number for hyperbolic surfaces). Our main ... More

Filling sets of curves on punctured surfacesAug 14 2015We study filling sets of simple closed curves on punctured surfaces. In particular we study lower bounds on the cardinality of sets of curves that fill and that pairwise intersect at most k times on surfaces with given genus and number of punctures. We ... More

On some regularity results for $\,2-D\,$ Euler equations and linear elliptic b.v. problemsFeb 04 2015About thirty years ago we looked for "minimal assumptions" on the data which guarantee that solutions to the $\,2-D\,$ evolution Euler equations in a bounded domain are classical. Classical means here that all the derivatives appearing in the equations ... More

Function spaces of coercivity for the fractional Laplacian in spaces of homogeneous typeMar 19 2018We combine dyadic analysis through Haar type wavelets defined on Christ's families of generalized cubes, and Lax-Milgram theorem, in order to prove existence of Green's functions for fractional Laplacians on some function spaces of vanishing small resolution ... More