Results for "Sébastien Renaux-Petel"
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Aspects of massive gravityDec 23 2015We report here on two works on Lorentz invariant massive gravity. In the first part, we derive the decoupling limit of massive gravity on de Sitter, relying on embedding de Sitter into an higher dimensional Minkowski spacetime. This enables us to identify ... More Non-Gaussian inflationary shapes in $G^3$ theories beyond HorndeskiJul 27 2014Sep 03 2014We consider the possible signatures of a recently introduced class of healthy theories beyond Horndeski models on higher-order correlators of the inflationary curvature fluctuation. Despite the apparent large number and complexity of the cubic interactions, ... More Geometrical Destabilization of InflationOct 05 2015Sep 20 2016We show the existence of a general mechanism by which heavy scalar fields can be destabilized during inflation, relying on the fact that the curvature of the field space manifold can dominate the stabilizing force from the potential and destabilize inflationary ... More On reaching the adiabatic limit in multi-field inflationMay 23 2014Dec 29 2014We calculate the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ in a class of recently proposed two-field no-scale inflationary models in supergravity. We show that, in order to obtain correct predictions, it is crucial to take into account ... More Perturbations in generalized multi-field inflationJan 07 2008May 31 2008We study the linear perturbations of multi-field inflationary models governed by a Lagrangian which is a general function of the scalar fields and of a global kinetic term combining their spacetime gradients with an arbitrary field space metric. Our analysis ... More Inflationary stochastic anomaliesJun 26 2018Feb 25 2019The stochastic approach aims at describing the long-wavelength part of quantum fields during inflation by a classical stochastic theory. It is usually formulated in terms of Langevin equations, giving rise to a Fokker-Planck equation for the probability ... More On rotarily transitive graphsMay 19 2016From the point of view of discrete geometry, the class of locally finite transitive graphs is a wide and important one. The subclass of Cayley graphs is of particular interest, as testifies the development of geometric group theory. Recall that Cayley ... More Ergodicity and indistinguishability in percolation theoryOct 04 2012Nov 13 2014This paper explores the link between the ergodicity of the clus-ter equivalence relation restricted to its infinite locus and the indis-tinguishability of infinite clusters. It is an important element of the dictionary connecting orbit equivalence and ... More On geometric aspects of the SUSY Fokas-Gel'fand immersion formulaJun 20 2017Mar 09 2018In this paper, we develop a new geometric characterization for the supersymmetric versions of the Fokas--Gel'fand formula for the immersion of soliton supermanifolds with two bosonic and two fermionic independent variables into Lie superalgebras. In order ... More Chern-Simons Invariants of Torus LinksMar 15 2010Jan 03 2011We compute the vacuum expectation values of torus knot operators in Chern-Simons theory, and we obtain explicit formulae for all classical gauge groups and for arbitrary representations. We reproduce a known formula for the HOMFLY invariants of torus ... More On the coldness of the local Hubble flow: the role of baryonsFeb 24 2010Jun 14 2010(Abridged) Our aim is to investigate whether the presence of baryons can have any significant influence on the properties of the local Hubble flow which has proved to be "cold". We use two cosmological zoom simulations in the standard LCDM cosmology with ... More Low energy scales of Kondo lattices: mean-field perspectiveMar 11 2009A review of the low temperature properties of Kondo lattice systems is presented within the mean-field approximation, focusing on the different characteristic energy scales. The Kondo temperature, T_K, and the Fermi liquid coherence energy, T_0, are analyzed ... More Directed Diffusion-Limited AggregationNov 13 2014Dec 22 2015In this paper, we define a directed version of the Diffusion-Limited-Aggregation model. We present several equivalent definitions in finite volume and a definition in infinite volume. We obtain bounds on the speed of propagation of information in infinite ... More A self-similar aperiodic set of 19 Wang tilesFeb 09 2018Jul 24 2018We define a Wang tile set $\mathcal{U}$ of cardinality 19 and show that the set $\Omega_\mathcal{U}$ of all valid Wang tilings $\mathbb{Z}^2\to\mathcal{U}$ is self-similar, aperiodic and is a minimal subshift of $\mathcal{U}^{\mathbb{Z}^2}$. Thus $\mathcal{U}$ ... More A Greedy Algorithm to Cluster SpecialistsSep 13 2016Several recent deep neural networks experiments leverage the generalist-specialist paradigm for classification. However, no formal study compared the performance of different clustering algorithms for class assignment. In this paper we perform such a ... More A counterexample to a question of Hof, Knill and SimonJul 05 2013In this article, we give a negative answer to a question of Hof, Knill and Simon (1995) concerning purely morphic sequences obtained from primitive morphism containing an infinite number of palindromes. Proven for the binary alphabet by B. Tan in 2007, ... More Conditional Moments of Anticipative $α$-Stable Markov ProcessesMay 14 2018The anticipative $\alpha$-stable autoregression of order 1 (AR(1)) is a stationary Markov process undergoing explosive episodes akin to bubbles in financial time series data. Although featuring infinite variance, integer conditional moments up to order ... More Torus Knots in Lens Spaces & Topological StringsAug 26 2013Jun 22 2014We study the invariant of knots in lens spaces defined from quantum Chern-Simons theory. By means of the knot operator formalism, we derive a generalization of the Rosso-Jones formula for torus knots in L(p,1). In the second part of the paper, we propose ... More Substitutive structure of Jeandel-Rao aperiodic tilingsAug 23 2018We describe the substitutive structure of Jeandel-Rao aperiodic Wang tilings $\Omega_0$. We introduce twelve sets of Wang tiles $\{\mathcal{T}_{i}\}_{1\leq i\leq 12}$ together with their associated Wang shifts $\{\Omega_{i}\}_{1\leq i\leq 12}$. Using ... More Weak Mixing and Analyticity of the Pressure in the Ising ModelMay 30 2019Jun 20 2019We prove that the pressure (or free energy) of the finite range ferromagnetic Ising model on $\mathbb{Z}^d$ is analytic as a function of both the inverse temperature $\beta$ and the magnetic field $h$ whenever the model has the exponential weak mixing ... More Cellular automata on a $G$-setMay 26 2011We extend the usual definition of cellular automaton on a group in order to deal with a new kind of cellular automata, like cellular automata in the hyperbolic plane and we explore some properties of these cellular automata. This definition also allows ... More Improved bounds for reduction to depth 4 and depth 3Apr 21 2013May 16 2014Koiran showed that if a $n$-variate polynomial of degree $d$ (with $d=n^{O(1)}$) is computed by a circuit of size $s$, then it is also computed by a homogeneous circuit of depth four and of size $2^{O(\sqrt{d}\log(d)\log(s))}$. Using this result, Gupta, ... More Viscoelastic flows with conservation lawsAug 09 2019We propose in this work the first symmetric hyperbolic system of conservation laws to describe viscoelastic flows of Maxwell fluids, i.e. fluidswith memory that are characterized by one relaxation-time parameter. Precisely, the system of quasilinear PDEs ... More A Markov partition for Jeandel-Rao aperiodic Wang tilingsMar 14 2019We define a Markov partition for a $\mathbb{Z}^2$-rotation on the 2-dimensional torus whose associated symbolic dynamical system is a minimal and aperiodic Wang shift defined by 19 Wang tiles. We define another partition for another $\mathbb{Z}^2$-rotation ... More Convex Optimization: Algorithms and ComplexityMay 20 2014Nov 16 2015This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. Starting from the fundamental theory of black-box optimization, the material progresses towards recent advances in structural optimization ... More Locally infinite graphs and symmetriesJan 05 2017When one studies geometric properties of graphs, local finiteness is a common implicit assumption, and that of transitivity a frequent explicit one. By compactness arguments, local finiteness guarantees several regularity properties. It is generally easy ... More Weak Mixing and Analyticity of the Pressure in the Ising ModelMay 30 2019We prove that the pressure (or free energy) of the finite range ferromagnetic Ising model on $\mathbb{Z}^d$ is analytic as a function of both the inverse temperature $\beta$ and the magnetic field $h$ whenever the model has the exponential weak mixing ... More Substitutive structure of Jeandel-Rao aperiodic tilingsAug 23 2018Apr 11 2019We describe the substitutive structure of Jeandel-Rao aperiodic Wang tilings $\Omega_0$. We introduce twelve sets of Wang tiles $\{\mathcal{T}_{i}\}_{1\leq i\leq 12}$ together with their associated Wang shifts $\{\Omega_{i}\}_{1\leq i\leq 12}$. Using ... More A self-similar aperiodic set of 19 Wang tilesFeb 09 2018Jul 10 2019We define a Wang tile set $\mathcal{U}$ of cardinality 19 and show that the set $\Omega_\mathcal{U}$ of all valid Wang tilings $\mathbb{Z}^2\to\mathcal{U}$ is self-similar, aperiodic and is a minimal subshift of $\mathcal{U}^{\mathbb{Z}^2}$. Thus $\mathcal{U}$ ... More Supersymmetric and R symmetric vacua in Wess-Zumino modelsAug 16 2007In the context of supersymmetric Wess-Zumino models with an R symmetry, we find some simple conditions on the R-charge content of the theory that imply the presence or absence of supersymmetric and R-symmetric vacua. The main result of this work is that ... More $3$-dimensional Continued Fraction Algorithms Cheat SheetsNov 26 2015Multidimensional Continued Fraction Algorithms are generalizations of the Euclid algorithm and find iteratively the gcd of two or more numbers. They are defined as linear applications on some subcone of $\mathbb{R}^d$. We consider multidimensional continued ... More Inkjet-printed vertically emitting solid-state organic lasersMay 25 2016In this paper, we show that Inkjet Printing can be successfully applied to external-cavity vertically-emitting thin-film organic lasers, and can be used to generate a diffraction-limited output beam with an output energy as high as 33.6 uJ with a slope ... More A Scalable Byzantine GridOct 17 2012Modern networks assemble an ever growing number of nodes. However, it remains difficult to increase the number of channels per node, thus the maximal degree of the network may be bounded. This is typically the case in grid topology networks, where each ... More Electron-phonon scattering in topological insulatorsMar 01 2011We formulate and apply a theory of electron-phonon interactions for the surface state of a strong topological insulator. Phonons are modelled using an isotropic elastic continuum theory with stress-free boundary conditions and interact with the Dirac ... More A Chaining Algorithm for Online Nonparametric RegressionFeb 26 2015Jul 01 2015We consider the problem of online nonparametric regression with arbitrary deterministic sequences. Using ideas from the chaining technique, we design an algorithm that achieves a Dudley-type regret bound similar to the one obtained in a non-constructive ... More Refined Lower Bounds for Adversarial BanditsMay 24 2016Feb 27 2017We provide new lower bounds on the regret that must be suffered by adversarial bandit algorithms. The new results show that recent upper bounds that either (a) hold with high-probability or (b) depend on the total lossof the best arm or (c) depend on ... More Reasons and Means to Model Preferences as IncompleteJan 05 2018Literature involving preferences of artificial agents or human beings often assume their preferences can be represented using a complete transitive binary relation. Much has been written however on different models of preferences. We review some of the ... More A Bayesian Clearing Mechanism for Combinatorial AuctionsDec 14 2017Nov 16 2018We cast the problem of combinatorial auction design in a Bayesian framework in order to incorporate prior information into the auction process and minimize the number of rounds to convergence. We first develop a generative model of agent valuations and ... More Safe Reinforcement Learning Using Robust MPCJun 10 2019Reinforcement Learning (RL) has recently impressed the world with stunning results in various applications. While the potential of RL is now well-established, many critical aspects still need to be tackled, including safety and stability issues. These ... More A note on Lang's conjecture for quotients of bounded domainsSep 07 2018Dec 13 2018It was conjectured by Lang that a complex projective manifold is Kobayashi hyperbolic if and only if it is of general type together with all of its subvarieties. We verify this conjecture for projective manifolds whose universal cover carries a bounded, ... More