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Online Sampling from Log-Concave DistributionsFeb 21 2019Given a sequence of convex functions $f_0, f_1, \ldots, f_T$, we study the problem of sampling from the Gibbs distribution $\pi_t \propto e^{-\sum_{k=0}^t f_k}$ for each epoch $t$ in an online manner. This problem occurs in applications to machine learning, ... More
Existence of densities for stochastic evolution equations driven by fractional Brownian motionFeb 21 2019In this work, we prove a version of H\"{o}rmander's theorem for a stochastic evolution equation driven by a trace-class fractional Brownian motion with Hurst exponent $\frac{1}{2} < H < 1$ and an analytic semigroup $\{S(t); t \ge 0\}$ on a given separable ... More
On persistent homology of random Čech complexesFeb 21 2019The paper studies the relation between critical simplices and persistence diagrams of the \v{C}ech filtration. We show that adding a critical $k$-simplex into the filtration corresponds either to a point in the $k$th persistence diagram or a point in ... More
Derivation of viscous Burgers equations from weakly asymmetric exclusion processesFeb 21 2019We consider weakly asymmetric exclusion processes whose initial density profile is a small perturbation of a constant. We show that in the diffusive time-scale, in all dimensions, the density defect evolves as the solution of a viscous Burgers equation. ... More
Kac Interaction Clusters: A Bilinear Coagulation Equation and Phase TransitionFeb 20 2019We consider the interaction clusters for Kac's model of a gas with quadratic interaction rates, and show that they behave as coagulating particles with a bilinear coagulation kernel. In the large particle number limit the distribution of the interaction ... More
Hopf's lemma for viscosity solutions to a class of non-local equations with applicationsFeb 20 2019We consider a large family of non-local equations featuring Markov generators of L\'evy processes, and establish a non-local Hopf's lemma and a variety of maximum principles for viscosity solutions. We then apply these results to study the principal eigenvalue ... More
Gain function approximation in the Feedback Particle FilterFeb 19 2019This paper is concerned with numerical algorithms for the problem of gain function approximation in the feedback particle filter. The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The numerical problem ... More
Statistical inference for a partially observed interacting system of Hawkes processesFeb 19 2019We observe the actions of a $K$ sub-sample of $N$ individuals up to time $t$ for some large $K<N$. We model the relationships of individuals by i.i.d. Bernoulli($p$)-random variables, where $p\in (0,1]$ is an unknown parameter. The rate of action of each ... More
On the convergence of stochastic transport equations to a deterministic parabolic oneFeb 19 2019A stochastic transport linear equation (STLE) with multiplicative space-time dependent noise is studied. It is shown that, under suitable assumptions on the noise, a multiplicative renormalization leads to convergence of the solutions of STLE to the solution ... More
Moderate deviations of subgraph counts in the Erdős-Rényi random graphs $G(n,m)$ and $G(n,p)$Feb 18 2019The main contribution of this article is an asymptotic expression for the rate associated with moderate deviations of subgraph counts in the Erd\H{o}s-R\'enyi random graph $G(n,m)$. Our approach is based on applying Freedman's inequalities for the probability ... More
Expansion of a filtration with a stochastic process: the information driftFeb 18 2019When expanding a filtration with a stochastic process it is easily possible for semimartingale no longer to remain semimartingales in the enlarged filtration. Y. Kchia and P. Protter indicated a way to avoid this pitfall in 2015, but they were unable ... More
Mesoscopic central limit theorem for the circular beta-ensembles and applicationsFeb 18 2019We give a simple proof of a central limit theorem for linear statistics of the Circular beta-ensembles which is valid at almost arbitrary mesoscopic scale and for functions of class C^3. As a consequence, using a coupling introduced by Valko and Virag, ... More
A Wong-Zakai Approximation of Stochastic Differential Equations Driven by a General SemimartingaleFeb 18 2019We examine a Wong-Zakai type approximation of a family of stochastic differential equations driven by a general cadlag semimartingale. For such an approximation, compared with the pointwise convergence result by Kurtz, Pardoux and Protter [12, Theorem ... More
Optimal Scaling and Shaping of Random Walk Metropolis via Diffusion Limits of Block-I.I.D. TargetsFeb 18 2019This work extends Roberts et al. (1997) by considering limits of Random Walk Metropolis (RWM) applied to block IID target distributions, with corresponding block-independent proposals. The extension verifies the robustness of the optimal scaling heuristic, ... More
Random polytopes and the wet part for arbitrary probability distributionsFeb 18 2019We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ points from an arbitrary probability measure in $\mathbf{R}^d$ relates to the wet part of that measure. This extends classical results for the uniform distribution ... More
Homogenization for Generalized Langevin Equations with Applications to Anomalous DiffusionFeb 18 2019We study homogenization for a class of generalized Langevin equations (GLEs) with state-dependent coefficients and exhibiting multiple time scales. In addition to the small mass limit, we focus on homogenization limits, which involve taking to zero the ... More
Aggregated test of independence based on HSIC measuresFeb 18 2019Dependence measures based on reproducing kernel Hilbert spaces, also known as Hilbert-Schmidt Independence Criterion and denoted HSIC, are widely used to statistically decide whether or not two random vectors are dependent. Recently, non-parametric HSIC-based ... More
Reformulation of Laplacian-$b$ motion in terms of stochastic Komatu-Loewner evolution in the chordal caseFeb 18 2019We investigate the relation between the Laplacian-$b$ motion and stochastic Komatu-Loewner evolution (SKLE) on multiply connected subdomains of the upper half-plane, both of which are analogues to SLE. In particular, we show that, if the driving function ... More
On the slit motion obeying chordal Komatu-Loewner equation with finite explosion timeFeb 18 2019This paper studies the behavior of solutions near the explosion time to the chordal Komatu-Loewner equation for slits, motivated by the preceding studies by Bauer and Friedrich (2008) and by Chen and Fukushima (2018). The solution to this equation represents ... More
A note on the total curvature of confined equilateral quadrilateralsFeb 17 2019In this note, we prove that the total expected curvature for random spatial equilateral quadrilaterals with diameter at most $r$ decreases as $r$ increases. To do so, we prove several curvature monotonicity inequalities and stochastic ordering lemmas ... More
Repartition of the quasi-stationary distribution and first exit point density for a double-well potentialFeb 17 2019Let $f: \mathbb R^{d} \to \mathbb R$ be a smooth function and $(X_t)_{t\ge 0}$ be the stochastic process solution to the overdamped Langevin dynamics $$d X_t = -\nabla f(X_t) d t + \sqrt{h} \ d B_t.$$ Let $\Omega\subset \mathbb R^d$ be a smooth bounded ... More
A functional limit theorem for coin tossing Markov chainsFeb 17 2019We prove a functional limit theorem for Markov chains that, in each step, move up or down by a possibly state dependent constant with probability $1/2$, respectively. The theorem entails that the law of every one-dimensional regular continuous strong ... More
Prophet inequality for bipartite matching: merits of being simple and non adaptiveFeb 17 2019We consider Bayesian online selection problem of a matching in bipartite graphs, i.e., online weighted matching problem with edge arrivals where online algorithm knows distributions of weights, that corresponds to the intersection of two matroids in [Kleinberg ... More
Hydrostatic limit for exclusion process with slow boundary revisitedFeb 17 2019We revisit in this short article the hydrostatic limit for the exclusion process with slow boundary. The original proof of this result relies on estimates of the correlation functions. We achieve the same result based on analysis of two different time ... More
Solving the 4NLS with white noise initial dataFeb 16 2019We construct global-in-time singular dynamics for the (renormalized) cubic fourth order nonlinear Schr\"odinger equation on the circle, having the white noise measure as an invariant measure. For this purpose, we introduce the "random-resonant / nonlinear ... More
Local $L^{p}$-solution for semilinear heat equation with fractional noiseFeb 16 2019We study the $L^{p}$-solutions for the semilinear heat equation with unbounded coefficients and driven by a infinite dimensional fractional Brownian motion with self-similarity parameter $H > 1/2$. Existence and uniqueness of local mild solutions are ... More
Group testing: an information theory perspectiveFeb 15 2019The group testing problem concerns discovering a small number of defective items within a large population by performing tests on pools of items. A test is positive if the pool contains at least one defective, and negative if it contains no defectives. ... More
Existence, uniqueness and regularity for the stochastic Ericksen-Leslie equationFeb 15 2019We investigate existence and uniqueness for the stochastic liquid crystal flow driven by colored noise on the two-dimensional torus. After giving a natural uniqueness criterion, we prove local solvability in $L^p$-based spaces, for every $p>2.$ Thanks ... More
Pathwise asymptotics for Volterra type rough volatility modelsFeb 15 2019We study fractional stochastic volatility models in which the volatility process is a positive continuous function $\sigma$ of a continuous fractional Volterra stochastic process $\hat B$. We establish a pathwise small-noise large deviation principle ... More
On Skorokhod Problem with Two RCLL Reflecting Completely Separated BarriersFeb 15 2019In this paper we deal with Skorokhod problem for right continuous left limits (rcll) barriers. We prove the existence and uniqueness of the solution when the barriers are only supposed to be rcll and completely separated. Then, we apply our result to ... More
Quenched invariance principle for random walks among random degenerate conductancesFeb 15 2019We consider the random conductance model in a stationary and ergodic environment. Under suitable moment conditions on the conductances and their inverse, we prove a quenched invariance principle for the random walk among the random conductances. The moment ... More
Effective distribution of codewords for Low Density Parity Check Cycle codes in the presence of disorderFeb 15 2019We review the zeta-function representation of codewords allowed by a parity-check code based on a bipartite graph, and then investigate the effect of disorder on the effective distribution of codewords. The randomness (or disorder) is implemented by sampling ... More
Scale-free percolation in continuum space: quenched degree and clustering coefficientFeb 15 2019Spatial random graphs capture several important properties of real-world networks. We prove quenched results for the continuum space version of scale-free percolation introduced in [DW18]. This is an undirected inhomogeneous random graph whose vertices ... More
Weak monotone rearrangement on the lineFeb 15 2019Weak optimal transport has been recently introduced by Gozlan et al. The original motivation stems from the theory of geometric inequalities; further applications concern numerics of martingale optimal transport and stability in mathematical finance. ... More
Stochastic homogenization of the Landau-Lifshitz-Gilbert equationFeb 15 2019Following the ideas of V. V. Zhikov and A. L. Pyatnitski, and more precisely the stochastic two-scale convergence, this paper establishes a homogenization theorem in a stochastic setting for two nonlinear equations : the equation of harmonic maps into ... More
On the Euler--Maruyama scheme for degenerate stochastic differential equations with non-sticky boundary conditionFeb 15 2019The aim of this paper is to study weak and strong convergence of the Euler--Maruyama scheme for a solution of one-dimensional degenerate stochastic differential equation $\mathrm{d} X_t=\sigma(X_t) \mathrm{d} W_t$ with non-sticky boundary condition. For ... More
Generalized semimodularity: order statisticsFeb 14 2019A notion of generalized $n$-semimodularity is introduced, which extends that of (sub/super)mod\-ularity in four ways at once. The main result of this paper, stating that every generalized $(n\colon\!2)$-semimodular function on the $n$th Cartesian power ... More
The Wasserstein Distances Between Pushed-Forward Measures with Applications to Uncertainty QuantificationFeb 14 2019Feb 20 2019In the study of dynamical and physical systems, the input parameters are often uncertain or randomly distributed according to a measure $\varrho$. The system's response $f$ pushes forward $\varrho$ to a new measure $f\circ \varrho$ which we would like ... More
The Wasserstein Distances Between Pushed-Forward Measures with Applications to Uncertainty QuantificationFeb 14 2019In the study of dynamical and physical systems, the input parameters are often uncertain or randomly distributed according to a measure $\varrho$. The system's response $f$ pushes forward $\varrho$ to a new measure $f\circ \varrho$ which we would like ... More
Pathwise Stochastic Control with Applications to Robust FilteringFeb 14 2019We study the problem of pathwise stochastic optimal control, where the optimization is performed for each fixed realisation of the driving noise, by phrasing the problem in terms of the optimal control of rough differential equations. We investigate the ... More
A simple proof of the Seneta-Heyde norming for branching random walks under optimal assumptionsFeb 14 2019We introduce a set of tools which simplify and streamline the proofs of limit theorems concerning near-critical particles in branching random walks under optimal assumptions. We exemplify our method by giving another proof of the Seneta-Heyde norming ... More
Subgaussianity is hereditarily determinedFeb 14 2019Let $n$ be a positive integer, let $\boldsymbol{X}=(X_1,\dots,X_n)$ be a random vector in $\mathbb{R}^n$ with bounded entries, and let $(\theta_1,\dots,\theta_n)$ be a vector in $\mathbb{R}^n$. We show that the subgaussian behavior of the random variable ... More
Multiple barrier-crossings of an Ornstein-Uhlenbeck diffusion in consecutive periodsFeb 14 2019We investigate the joint distribution and the multivariate survival functions for the maxima of an Ornstein-Uhlenbeck (OU) process in consecutive time-intervals. A PDE method, alongside an eigenfunction expansion is adopted, with which we are able to ... More
Shrinking scale equidistribution for monochromatic random waves on compact manifoldsFeb 14 2019We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random function. With ... More
On the number of crossings in a random labelled tree with vertices in convex positionFeb 14 2019We prove that the number of crossings in a random labelled tree with vertices in convex position is asymptotically Gaussian with mean $ n^2/6$ and variance $ n^3/45$. A similar result is proved for points in general position under mild constraints.
Asymptotic expansion of the density for hypoelliptic rough differential equationFeb 14 2019We study a rough differential equation driven by fractional Brownian motion with Hurst parameter $H$ $(1/4<H \le 1/2)$. Under H\"ormander's condition on the coefficient vector fields, the solution has a smooth density for each fixed time. Using Watanabe's ... More
Global solutions to the supercooled Stefan problem with blow-ups: regularity and uniquenessFeb 14 2019We consider the supercooled Stefan problem, which captures the freezing of a supercooled liquid, in one space dimension. A probabilistic reformulation of the problem allows to define global solutions, even in the presence of blow-ups of the freezing rate. ... More
Reconstructing Trees from TracesFeb 13 2019We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree being a path. ... More
The fluid limit of a random graph model for a shared ledgerFeb 13 2019A shared ledger is a record of transactions that can be updated by any member of a group of users. The notion of independent and consistent record-keeping in a shared ledger is important for blockchain and more generally for distributed ledger technologies. ... More
Semigroups for One-Dimensional Schrödinger Operators with Multiplicative White NoiseFeb 13 2019Let $ H:=-\tfrac12\Delta+V$ be a one-dimensional continuum Schr\"odinger operator. Consider ${\hat H}:= H+\xi$, where $\xi$ is a Gaussian white noise. We prove that if the potential $V$ is locally integrable, bounded below, and grows faster than $\log$ ... More
Heat Kernel Estimates for Fractional Heat EquationFeb 13 2019We study the long-time behavior of the Cesaro means of fundamental solutions for fractional evolution equations corresponding to random time changes in the Brownian motion and other Markov processes. We consider both stable subordinators leading to equations ... More
Chain-referral sampling on Stochastic Block ModelsFeb 13 2019We are motivated by the study of `hidden populations', in which all frameworks including size or membership are unknown. The discovery of the hidden population is made possible by assuming that its members are connected in a social network by their relationships. ... More
The scaling limits for Wiener sausages in random environmentsFeb 13 2019We consider the statistical mechanics of a random polymer with random walks and disorders in $\mathbb{Z}^d$. The walk collects random disorders along the way and gets nothing if it visits the same site twice. In the continuum and weak disorder regime, ... More
Gradient Gibbs measures for the SOS model with countable values on a Cayley treeFeb 13 2019We consider an SOS (solid-on-solid) model, with spin values from the set of all integers, on a Cayley tree of order k and are interested in translation-invariant gradient Gibbs measures (GGMs) of the model. Such a measure corresponds to a boundary law ... More
Random positive operator valued measuresFeb 13 2019We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, obtaining limiting eigenvalue distributions ... More
Transport processes on networked topologiesFeb 13 2019Consider a particle whose position evolves along the edges of a network. One definition for the displacement of a particle is the length of the shortest path on the network between the current and initial positions of the particle. Such a definition fails ... More
On the growth of random planar trees and maps with a prescribed degree sequenceFeb 12 2019For non-negative integers $(d_n(k))_{k \ge 1}$ such that $\sum_{k \ge 1} d_n(k) = n$, we sample a planar tree with $n$ inner vertices uniformly at random amongst those which have $d_n(k)$ vertices with out-degree $k$ for every $k \ge 1$ and we study its ... More
Parameter and dimension dependence of convergence rates to stationarity for Reflecting Brownian MotionsFeb 12 2019We obtain rates of convergence to stationarity in L^1-Wasserstein distance for a d-dimensional reflected Brownian motion (RBM) in the nonnegative orthant that are explicit in the dimension and the system parameters. The results are then applied to a class ... More
Complete resource pooling of a load balancing policy for a network of battery swapping stationsFeb 12 2019To reduce carbon emission in the transportation sector, there is currently a steady move taking place to an electrified transportation system. This brings about various issues for which a promising solution involves the construction and operation of a ... More
Bivariate distributions with ordered marginalsFeb 12 2019This paper provides a characterization of all possible dependency structures between two stochastically ordered random variables. The answer is given in terms of all possible copulas that are compatible with the stochastic order. The extremal values for ... More
Polynomial behavior in mean of stochastic skew-evolution semiflowsFeb 12 2019In this paper, we are interested in the more general concept of a polynomial (in)stability in mean in which the polynomial behaviour in the classical sense is replaced by a weaker requirement with respect to some probability measure. This concept includes ... More
The Poincaré inequality and quadratic transportation-variance inequalitiesFeb 12 2019Feb 14 2019It is known that the Poincar\'e inequality is equivalent to the quadratic transportation-variance inequality (namely $W_2^2(f\mu,\mu) \leqslant C_V \mathrm{Var}_\mu(f)$), see Jourdain \cite{Jourdain} and most recently Ledoux \cite{Ledoux18}. We give an ... More
The Poincaré inequality and quadratic transportation-variance inequalitiesFeb 12 2019It is known that the Poincar\'e inequality is equivalent to the quadratic transportation-variance inequality (namely $W_2^2(f\mu,\mu) \leqslant C_V \mathrm{Var}_\mu(f)$), see Ledoux \cite{Ledoux18} most recently. We give an alternative proof to this fact. ... More
Bivariate fluctuations for the number of arithmetic progressions in random setsFeb 11 2019We study arithmetic progressions $\{a,a+b,a+2b,\dots,a+(\ell-1) b\}$, with $\ell\ge 3$, in random subsets of the initial segment of natural numbers $[n]:=\{1,2,\dots, n\}$. Given $p\in[0,1]$ we denote by $[n]_p$ the random subset of $[n]$ which includes ... More
Sandpile dynamics on periodic tiling graphsFeb 11 2019Sandpile dynamics are considered on graphs constructed from periodic plane and space tilings by assigning a growing piece of the tiling either torus or open boundary conditions. A method of computing the Green's function and spectral gap is given for ... More
Renormalizing the Kardar-Parisi-Zhang equation in $d\geq 3$ in weak disorderFeb 11 2019We study Kardar-Parisi-Zhang equation in spatial dimension 3 or larger driven by a Gaussian space-time white noise with a small convolution in space. When the noise intensity is small, it is known that the solutions converge to a random limit as the smoothing ... More
Universal tail profile of Gaussian multiplicative chaosFeb 11 2019In this article we study the tail probability of the mass of Gaussian multiplicative chaos. With the novel use of a Tauberian argument and Goldie's implicit renewal theorem, we provide a unified approach to general log-correlated Gaussian fields in arbitrary ... More
Limit theory for the number of isolated and extreme points in hyperbolic random geometric graphsFeb 11 2019Given $\alpha \in (0, \infty)$ and $r \in (0, \infty)$, let ${\cal D}_{r, \alpha}$be the disc of radius $r$ in the hyperbolic plane having curvature $-\alpha^2$. Consider the Poisson point process having uniform intensity density on ${\cal D}_{R, \alpha}$, ... More
Semimartingales on Duals of Nuclear SpacesFeb 11 2019This work is devoted to the study of semimartingales and cylindrical semimartingales in infinite dimensional spaces. We start by establishing conditions for a cylindrical semimartingale in the strong dual $\Phi'$ of a general nuclear space $\Phi$ to have ... More
A Skorokhod Criterion for the Existence of SemimartingalesFeb 11 2019We prove the existence of quasi-left continuous semimartingales with continuous local semimartingale characteristics which satisfy a Lyapunov-type or a linear growth condition, where latter takes the whole history of the paths into consideration. The ... More
Conditional Tail Independence in Archimedean Copula ModelsFeb 11 2019Consider a random vector $U$, whose distribution function coincides in its upper tail with that of an Archimedean copula. We report the fact that the conditional distribution of $U$, conditional on one of its components, has under a mild condition on ... More
Stationary Distributions and Convergence for M/M/1 Queues in Interactive Random EnvironmentFeb 11 2019We study a Markovian single-server queue in interactive random environments. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depends on the queue length. We consider two types ... More
Sharp Cheeger-Buser type inequalities in $ \mathsf{RCD}(K,\infty)$ spacesFeb 11 2019The goal of the paper is to sharpen and generalise bounds involving the Cheeger's isoperimetric constant $h$ and the first eigenvalue $\lambda_{1}$ of the Laplacian. \\A celebrated lower bound of $\lambda_{1}$ in terms of $h$, $\lambda_{1}\geq h^{2}/4$, ... More
Tails and probabilities for $p$-outliersFeb 11 2019The task for a general and useful classification of the heaviness of the tails of probability distributions still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be described ... More
High-dimensional central limit theorems for homogeneous sumsFeb 11 2019This paper develops a quantitative version of de Jong's central limit theorem for homogeneous sums in a high-dimensional setting. More precisely, under appropriate moment assumptions, we establish an upper bound for the Kolmogorov distance between a multi-dimensional ... More
From fractals in external DLA to internal DLA on fractalsFeb 11 2019We present an unified approach on the behavior of two random growth models (external DLA and internal DLA) on infinite graphs, the second one being an internal counterpart of the first one. Even though the two models look pretty similar, their behavior ... More
A Short Note on Concentration Inequalities for Random Vectors with SubGaussian NormFeb 11 2019In this note, we derive concentration inequalities for random vectors with subGaussian norm (a generalization of both subGaussian random vectors and norm bounded random vectors), which are tight up to logarithmic factors.
Lorentzian polynomialsFeb 11 2019We study the class of Lorentzian polynomials. The class contains homogeneous stable polynomials as well as volume polynomials of convex bodies and projective varieties. We prove that the Hessian of a nonzero Lorentzian polynomial has exactly one positive ... More
The Optimal Approximation Factor in Density EstimationFeb 10 2019Consider the following problem: given two arbitrary densities $q_1,q_2$ and a sample-access to an unknown target density $p$, find which of the $q_i$'s is closer to $p$ in total variation. A remarkable result due to Yatracos shows that this problem is ... More
Optimal bilinear control of stochastic nonlinear Schrödinger equations: mass-(sub)critical caseFeb 10 2019We study optimal bilinear control problems for stochastic nonlinear Schr\"odinger equations in both the mass subcritical and critical case. For general initial data of the minimal L2 regularity, we prove the existence and first order Lagrange condition ... More
Integrability and regularity of the flow of stochastic differential equations with jumpsFeb 10 2019We derive sufficient conditions for the differentiability of all orders for the flow of stochastic differential equations with jumps, and prove related $L^p$-integrability results for all orders. Our results extend similar results obtained in [Kun04] ... More
When do factors promoting balanced selection also promote population persistence? A demographic perspective on Gillespie's SAS-CFF modelFeb 09 2019Classical stochasticity demography predicts that environmental stochasticity reduces population growth rates and, thereby, can increase extinction risk. In contrast, the SAS-CFF model demonstrates that environmental stochasticity can promote genetic diversity. ... More
Stability of Mc Kean-Vlasov stochastic differential equations and applicationsFeb 09 2019We consider Mc Kean-Vlasov stochastic differential equations (MVSDEs), which are SDEs where the drift and diffusion coefficients depend not only on the state of the unknown process but also on its probability distribution. This type of SDEs was studied ... More
On the error bound in the normal approximation for Jack measuresFeb 09 2019Feb 13 2019In this paper, we obtain uniform and non-uniform bounds on the Kolmogorov distance in the normal approximation for Jack deformations of the character ratio, by using Stein's method and zero-bias couplings. Our uniform bound comes very close to that conjectured ... More
On the error bound in the normal approximation for Jack measuresFeb 09 2019In this paper, we obtain uniform and non-uniform bounds on the Kolmogorov distance in the normal approximation for Jack deformations of the character ratio, by using Stein's method and zero-bias couplings. Our uniform bound comes very close to that conjectured ... More
A stochastic version of Stein Variational Gradient Descent for efficient samplingFeb 09 2019We propose in this work RBM-SVGD, a stochastic version of Stein Variational Gradient Descent (SVGD) method for efficiently sampling from a given probability measure and thus useful for Bayesian inference. The method is to apply the Random Batch Method ... More
Percolation in majority dynamicsFeb 09 2019We consider two-dimensional dependent dynamical site percolation where sites perform majority dynamics. We introduce the critical percolation function at time t as the infimum density with which one needs to begin in order to obtain an infinite open component ... More
Exchangeable and Sampling Consistent Distributions on Rooted Binary TreesFeb 08 2019We introduce a notion of finite sampling consistency for phylogenetic trees and show that the set of finitely sampling consistent and exchangeable distributions on n leaf phylogenetic trees is a polytope. We use this polytope to show that the set of all ... More
Exponential decay of correlations in the two-dimensional random field Ising model at zero temperatureFeb 08 2019We study random field Ising model on $\mathbb Z^2$ where the external field is given by i.i.d.\ Gaussian variables with mean zero and positive variance. We show that at zero temperature the effect of boundary conditions on the magnetization in a finite ... More
Large deviations and entropy production in viscous fluid flowsFeb 08 2019We study the motion of a particle in a random time-dependent vector field defined by the 2D Navier-Stokes system with a noise. Under suitable non-degeneracy hypotheses we prove that the empirical measures of the trajectories of the pair (velocity field, ... More
Survival and extinction of epidemics on random graphs with general degreesFeb 08 2019In this paper, we establish the necessary and sufficient criterion for the contact process on Galton-Watson trees (resp. random graphs) to exhibit the phase of extinction (resp. short survival). We prove that the survival threshold $\lambda_1$ for a Galton-Watson ... More
Upper bounds on the percolation correlation lengthFeb 08 2019We study the size of the near-critical window for Bernoulli percolation on $\mathbb Z^d$. More precisely, we use a quantitative Grimmett-Marstrand theorem to prove that the correlation length, both below and above criticality, is bounded from above by ... More
Affine Invariant Covariance Estimation for Heavy-Tailed DistributionsFeb 08 2019In this work we provide an estimator for the covariance matrix of a heavy-tailed random vector. We prove that the proposed estimator $\widehat{\mathbf{S}}$ admits \textit{affine-invariant} bounds of the form $$(1-\varepsilon) \mathbf{S} \preccurlyeq \widehat{\mathbf{S}} ... More
Geometric convergence bounds for Markov chains in Wasserstein distance based on generalized drift and contraction conditionsFeb 08 2019Let $\{X_n\}_{n=0}^\infty$ denote an ergodic Markov chain on a general state space that has stationary distribution $\pi$. This article concerns upper bounds on the $L_1$-Wasserstein distance between the distribution of $X_n$ and $\pi$ in the case where ... More
Geometric stochastic heat equationsFeb 07 2019We consider a natural class of $\mathbf{R}^d$-valued one-dimensional stochastic PDEs driven by space-time white noise that is formally invariant under the action of the diffeomorphism group on $\mathbf{R}^d$. This class contains in particular the KPZ ... More
Geometric stochastic heat equationsFeb 07 2019Feb 11 2019We consider a natural class of $\mathbf{R}^d$-valued one-dimensional stochastic PDEs driven by space-time white noise that is formally invariant under the action of the diffeomorphism group on $\mathbf{R}^d$. This class contains in particular the KPZ ... More
Exponential ergodicity for stochastic equations of nonnegative processes with jumpsFeb 07 2019In this work, we study ergodicity of continuous time Markov processes on state space $\mathbb{R}_{\geq 0} := [0,\infty)$ obtained as unique strong solutions to stochastic equations with jumps. Our first main result establishes exponential ergodicity in ... More
Appendix To Limits For Partial Maxima Of Gaussian Random VectorsFeb 07 2019This appendix provides a short proof for sample path continuity of the Brownian motion induced by an arbitrary centered Gaussian measure on a separable Banach space, and also some perturbation results for the spectrum of compact self-adjoint operators ... More
Modified log-Sobolev inequalities for strong-Rayleigh measuresFeb 07 2019We establish universal modified log-Sobolev inequalities for reversible Markov chains on the boolean lattice $\{0,1\}^n$, under the only assumption that the invariant law $\pi$ satisfies a form of negative dependence known as the \emph{stochastic covering ... More
Random walk on dynamical percolationFeb 07 2019We consider the model of random walk on dynamical percolation introduced by Peres, Stauffer and Steif (2015). We obtain comparison results for this model for hitting and mixing times and for the spectral-gap and log-Sobolev constant with the corresponding ... More