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Random matrix products: Universality and least singular valuesFeb 08 2018We establish local universality of the $k$-point correlation functions associated with products of independent iid random matrices, as the sizes of the matrices tend to infinity, under a moment matching hypothesis. We also prove Gaussian limits for the ... More
Existence of two-step replica symmetry breaking for the spherical mixed p-spin glass at zero temperatureFeb 08 2018We provide the first examples of two-step replica symmetry breaking (2-RSB) models for the spherical mixed p-spin glass at zero temperature. Precisely, we show that for a certain class of mixtures, the Parisi measure at zero temperature is purely atomic ... More
Singular values of large non-central random matricesFeb 08 2018We study largest singular values of large random matrices, each with mean of a fixed rank $K$. Our main result is a limit theorem as the number of rows and columns approach infinity, while their ratio approaches a positive constant. It provides a decomposition ... More
Parametric inference for multidimensional hypoelliptic diffusion with full observationsFeb 08 2018Multidimensional hypoelliptic diffusions arise naturally as models of neuronal activity. Estimation in those models is complex because of the degenerate structure of the diffusion coefficient. We build a consistent estimator of the drift and variance ... More
Multivariate subordination of stable processesFeb 08 2018This article is devoted to some time-changed stochastic models based on multivariate stable processes. The considered models have several advantages in comparison with classical time-changed Brownian motions - for instance, it turns out that they are ... More
Relative perturbation bounds with applications to empirical covariance operatorsFeb 08 2018The goal of this paper is to establish relative perturbation bounds, tailored for empirical covariance operators. Our main results are expansions for empirical eigenvalues and spectral projectors, leading to concentration inequalities and limit theorems. ... More
Serve the shortest queue and Walsh Brownian motionFeb 08 2018We study a single-server Markovian queueing model with $N$ customer classes in which priority is given to the shortest queue. Under a critical load condition, we establish the diffusion limit of the workload and queue length processes in the form of a ... More
Negative Binomial Construction of Random Discrete Distributions on the Infinite SimplexFeb 07 2018The Poisson-Kingman distributions, $\mathrm{PK}(\rho)$, on the infinite simplex, can be constructed from a Poisson point process having intensity density $\rho$ or by taking the ranked jumps up till a specified time of a subordinator with L\'evy density ... More
Probabilistic Non-asymptotic Analysis of Distributed AlgorithmsFeb 07 2018We present a new probabilistic analysis of distributed algorithms. Our approach relies on the theory of quasi-stationary distributions (QSD) recently developped by Champagnat and Villemonais. We give properties on the deadlock time and the distribution ... More
Self-stabilizing processeFeb 07 2018We construct `self-stabilizing' processes {Z(t), t $\in [t_0,t_1)$}. These are random processes which when `localized', that is scaled around t to a fine limit, have the distribution of an $\alpha$(Z(t))-stable process, where $\alpha$ is some given function ... More
Disconnection by level sets of the discrete Gaussian free field and entropic repulsionFeb 07 2018We derive asymptotic upper and lower bounds on the large deviation probability that the level set of the Gaussian free field on $Z^d$, d bigger or equal to three, below a given level disconnects the discrete blow-up of a compact set A from the boundary ... More
Large deviations of reaction fluxesFeb 07 2018Feb 08 2018We study a system of interacting particles that randomly react to form new particles. The reaction flux is the rescaled number of reactions that take place in a time interval. We prove a dynamic large-deviation principle for the reaction fluxes under ... More
The law of a point process of Brownian excursions in a domain is determined by the law of its traceFeb 07 2018We show the result that is stated in the title of the paper, which has consequences about decomposition of Brownian loop-soup clusters in two dimensions.
Statistical tests for daily and total precipitation volumes to be abnormally extremalFeb 07 2018In this paper, two approaches are proposed to the definition of abnormally extremal precipitation. These approaches are based on the negative binomial model for the distribution of duration of wet periods measured in days. This model demonstrates excellent ... More
Maintenance of diversity in a parasite population capable of persistence and reinfectionFeb 07 2018Motivated by observations in DNA data of the human cytomegalovirus, we study the dynamics and the maintenance of diversity in a hierarchical model of a two-type parasite population distributed over its (infected) hosts. The parasite is assumed to be capable ... More
Gundy-Varopoulos martingale transforms and their projection operators on manifolds and vector bundlesFeb 07 2018This paper proves the $L^p$ boundedness of generalized first order Riesz transforms obtained as conditional expectations of martingale transforms \`a la Gundy-Varopoulos for quite general diffusions on manifolds and vector bundles. Several specific examples ... More
Unique Quasi-Stationary Distribution, with a possibly stabilizing extinctionFeb 07 2018We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process conditioned to never ... More
An improved upper bound for critical value of the contact process on $\mathbb{Z}^d$ with $d\geq 3$Feb 07 2018In this paper we give an improved upper bound for critical value $\lambda_c$ of the basic contact process on the lattice $\mathbb{Z}^d$ with $d\geq 3$. As a direct corollary of out result, \[ \lambda_c\leq 0.384. \] when $d=3$.
Real zeros of random analytic functions associated with geometries of constant curvatureFeb 07 2018Feb 08 2018Let $\xi_0, \xi_1, \dots$ be i.i.d. random variables with zero mean and unit variance. We study the following four families of random analytic functions: $\sum_{k=0}^n \sqrt{\binom nk} \xi_k z^k$ (spherical polynomials), $\sum_{k=0}^\infty \sqrt{\frac{n^k}{k!}} ... More
Scaling limits of general population processes - Wright-Fisher and branching processes in random environmentFeb 07 2018Our motivation comes from the large population approximation of individual based models in population dynamics and population genetics. We propose a general method to investigate scaling limits of finite dimensional population size Markov chains to diffusion ... More
Impacts of Environmental Noises upon Asymptotic Behavior of SIRS ModelsFeb 07 2018In this paper, we are interested in the impacts of environmental noises on extinction and persistence for SIRS models in random environments. Our contributions consist in (i) giving some sufficient conditions on extinction (persistence) of the infectious ... More
Learning interacting particle systems: diffusion parameter estimation for aggregation equationsFeb 07 2018In this article, we study the parameter estimation of interacting particle systems subject to the Newtonian aggregation. Specifically, we construct an estimator $\widehat{\nu}$ with partial observed data to approximate the diffusion parameter $\nu$, and ... More
Second order backward SDE with random terminal timeFeb 06 2018Backward stochastic differential equations extend the martingale representation theorem to the nonlinear setting. This can be seen as path-dependent counterpart of the extension from the heat equation to fully nonlinear parabolic equations in the Markov ... More
De Finetti's theorem: rate of convergence in Kolmogorov distanceFeb 06 2018This paper provides a quantitative version of de Finetti strong law of large numbers. Here, we consider the convergence in law, metrized by the Kolmogorov distance. Our main result improve on existing literature: in particular, with respect to [5] we ... More
On the asymptotic of exit problems for controlled Markov diffusion processes with random jumps and vanishing diffusion termsFeb 06 2018In this paper, we study the asymptotic of exit problem for controlled Markov diffusion processes with random jumps and vanishing diffusion terms, where the random jumps are introduced in order to modify the evolution of the controlled diffusions by switching ... More
Dynkin isomorphism and Mermin--Wagner theorems for hyperbolic sigma models and recurrence of the two-dimensional vertex-reinforced jump processFeb 06 2018We prove the vertex-reinforced jump process (VRJP) is recurrent in two dimensions for any translation invariant finite range initial rates. Our proof has two main ingredients. The first is a direct connection between the VRJP and sigma models whose target ... More
Splitting models for multivariate count dataFeb 06 2018Considering discrete models, the univariate framework has been studied in depth compared to the multivariate one. This paper first proposes two criteria to define a sensu stricto multivariate discrete distribution. It then introduces the class of splitting ... More
One-sided continuity properties for the Schonmann projectionFeb 06 2018We consider the plus-phase of the two-dimensional Ising model below the critical temperature. In $1989$ Schonmann proved that the projection of this measure onto a one-dimensional line is not a Gibbs measure. After many years of continued research which ... More
On the structure of random graphs that are locally indistinguishable from a latticeFeb 06 2018We study the properties of finite graphs in which the ball of radius $r$ around each vertex induces a graph isomorphic to the ball of radius $r$ in some fixed vertex-transitive graph $F$. This is a natural extension of the study of regular graphs. We ... More
Roots of Polynomials and The Derangement ProblemFeb 06 2018We present a new killing-a-fly-with-a-sledgehammer proof of one of the oldest results in probability which says that the probability that a random permutation on $n$ elements has no fixed points tends to $e^{-1}$ as $n$ tends to infinity. Our proof stems ... More
Boundary representations of $λ$-harmonic and polyharmonic functions on treesFeb 06 2018On a countable tree $T$, allowing vertices with infinite degree, we consider an arbitrary stochastic irreducible nearest neighbour transition operator $P$. We provide a boundary integral representation for general eigenfunctions of $P$ with eigenvalue ... More
Hydrodynamic Limit for an Anharmonic Chain under Boundary TensionFeb 06 2018We study the hydrodynamic limit for a one dimensional isothermal anharmonic finite chain in Lagrangian coordinates with hyperbolic space-time scaling. The temperature is kept constant by putting the chain in contact with a heat bath, realised via a stochastic ... More
Random cliques in random graphsFeb 06 2018We show that for each $r\ge 4$, in a density range extending up to, and slightly beyond, the threshold for a $K_r$-factor, the copies of $K_r$ in the random graph $G(n,p)$ are randomly distributed, in the (one-sided) sense that the hypergraph that they ... More
Hidden regular variation, copula models, and the limit behavior of conditional excess risk measuresFeb 06 2018Risk measures like Marginal Expected Shortfall and Marginal Mean Excess quantify conditional risk and in particular, aid in the understanding of systemic risk. In many such scenarios, models exhibiting heavy tails in the margins and asymptotic tail independence ... More
Unbounded largest eigenvalue of large sample covariance matrices: Asymptotics, fluctuations and applicationsFeb 06 2018Given a large sample covariance matrix$S\_N=\frac 1n\Gamma\_N^{1/2}Z\_N Z\_N^*\Gamma\_N^{1/2}\, ,$where $Z\_N$ is a $N\times n$ matrix with i.i.d. centered entries, and $\Gamma\_N$ is a $N\times N$ deterministic Hermitian positive semidefinite matrix, ... More
Bounds for $L_p$-discrepancies of point distributions in compact metric spacesFeb 05 2018We consider finite point subsets (distributions) in compact connected metric measure spaces. The spaces under study are specialized by conditions on the volume of metric balls as a function of radii. These conditions are not hard and hold, particularly, ... More
On singular value distribution of large dimensional data matrices whose columns have different correlationsFeb 05 2018Suppose $\mathbf Y_n=(\mathbf y_1,\cdots,\mathbf y_n)$ is a $p\times n$ data matrix whose columns $\mathbf y_j, 1\leq j\leq n$ have different correlations. The asymptotic spectral property of $\mathbf S_n=\frac1n\mathbf Y_n\mathbf Y^*_n$ when $p$ increase ... More
A continuous time tug-of-war game for parabolic $p(x,t)$-Laplace type equationsFeb 02 2018We formulate a stochastic differential game in continuous time that represents the unique viscosity solution to a terminal value problem for a parabolic partial differential equation involving the normalized $p(x,t)$-Laplace operator. Our game is formulated ... More
On tails of symmetric and totally asymmetric $α$-stable distributionsFeb 02 2018We estimate up to universal constants tails of symmetric and totally asymmetric $\alpha$-stable distributions in terms of functions of the parameters of these distributions.
Stochastic Differential Equations with Critical DriftsJan 31 2018We construct a strong solution to the stochastic differential equation with additive noise when drift term belongs to $L^{q,1}([0,T],L^p_x)$ for $p,q\in (1,\infty)$ satisfying $\frac{2}{q}+\frac{d}{p} =1$. We also prove the Sobolev regularity of the stochastic ... More
Contextuality Analysis of the Double Slit Experiment (With a Glimpse Into Three Slits)Jan 31 2018The Contextuality-by-Default theory is illustrated on contextuality analysis of the idealized double-slit experiment. The system of contextually labeled random variables describing this experiment forms a cyclic system of rank 4, formally the same as ... More
On the computability of graphonsJan 31 2018We investigate the relative computability of exchangeable binary relational data when presented in terms of the distribution of an invariant measure on graphs, or as a graphon in either $L^1$ or the cut distance. We establish basic computable equivalences, ... More
Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operatorJan 30 2018We study the convergence of the graph Laplacian of a random geometric graph generated by an i.i.d. sample from a $m$-dimensional submanifold $M$ in $R^d$ as the sample size $n$ increases and the neighborhood size $h$ tends to zero. We show that eigenvalues ... More
Properties of additive functionals of Brownian motion with resettingJan 30 2018We study the distribution of time-additive functionals of reset Brownian motion, a variation of normal Brownian motion in which the path is interrupted at a given rate according to a Poisson process and placed back to a given reset position. For three ... More
A multi-scale limit of a randomly forced rotating $3$-D compressible fluidJan 29 2018We study a singular limit of a scaled compressible Navier--Stokes--Coriolis system driven by both a deterministic and stochastic forcing terms in three dimensions. If the Mach number is comparable to the Froude number with both proportional to say $\varepsilon\ll ... More
Second Order Asymptotic Properties for the Tail Probability of the Number of Customers in the M/G/1 Retrial QueueJan 29 2018When an explicit expression for a probability distribution function $F(x)$ can not be found, asymptotic properties of the tail probability function $\bar{F}(x)=1-F(x)$ are very valuable, since they provide approximations or bounds for system performance, ... More
Strong error analysis for stochastic gradient descent optimization algorithmsJan 29 2018Stochastic gradient descent (SGD) optimization algorithms are key ingredients in a series of machine learning applications. In this article we perform a rigorous strong error analysis for SGD optimization algorithms. In particular, we prove for every ... More
Nash inequality for Diffusion Processes Associated with Dirichlet DistributionsJan 28 2018For any $N\ge 2$ and $\alpha=(\alpha_1,\cdots, \alpha_{N+1})\in (0,\infty)^{N+1}$, let $\mu^{(N)}_{\alpha}$ be the Dirichlet distribution with parameter $\alpha$ on the set $\Delta^{ (N)}:= \{ x \in [0,1]^N:\ \sum_{1\le i\le N}x_i \le 1 \}.$ The multivariate ... More
Generalized Estimating Equation for the Student-t DistributionsJan 27 2018In \cite{KumarS15J2}, it was shown that a generalized maximum likelihood estimation problem on a (canonical) $\alpha$-power-law model ($\mathbb{M}^{(\alpha)}$-family) can be solved by solving a system of linear equations. This was due to an orthogonality ... More
Concentration without measureJan 26 2018Although there doesn't exist the Lebesgue measure in the ball $M$ of $C[0,1]$ with $p-$norm, the average values (expectation) $EY$ and variance $DY$ of some functionals $Y$ on $M$ can still be defined through the procedure of limitation from finite dimension ... More
Individual testing is optimal for nonadaptive group testing in the linear regimeJan 25 2018We consider nonadaptive probabilistic group testing in the linear regime, where each of n items is defective independently with probability p in (0,1), where p is a constant independent of n. We show that testing each item individually is optimal, in ... More
A randomized and fully discrete Galerkin finite element method for semilinear stochastic evolution equationsJan 25 2018In this paper the numerical solution of non-autonomous semilinear stochastic evolution equations driven by an additive Wiener noise is investigated. We introduce a novel fully discrete numerical approximation that combines a standard Galerkin finite element ... More
The transport equation and zero quadratic variation processesJan 24 2018We analyze the transport equation driven by a zero quadratic variation process. Using the stochastic calculus via regularization and the Malliavin calculus techniques, we prove the existence, uniqueness and absolute continuity of the law of the solution. ... More
Singular integrals of stable subordinatorJan 24 2018It is well known that $\int_{0}^{1} t^{-\theta} d t<\infty$ for $\theta \in (0,1)$ and $\int_{0}^{1} t^{-\theta} d t=\infty$ for $\theta \in [1,\infty)$. Since $t$ can be taken as an $\alpha$-stable subordinator with $\alpha=1$, it is natural to ask whether ... More
Sharp comparison of moments and the log-concave moment problemJan 23 2018This article investigates sharp comparison of moments for various classes of random variables appearing in a geometric context. In the first part of our work we find the optimal constants in the Khintchine inequality for random vectors uniformly distributed ... More
Asymptotics of Queue Length Distributions in Priority Retrial QueuesJan 22 2018We calculate asymptotics of the distribution of the number of customers in orbit in a two-class priority retrial $M/G/1$-type queueing model. In this model, priority customers wait in line while non-priority customers join an orbit and retry later. Although ... More
The exact Power Law for Buffon's needle landing near some Random Cantor SetsJan 21 2018Jan 29 2018In this paper, we study the Favard length of some random Cantor sets of Hausdorff dimension 1. We start with a unit disk in the plane and replace the unit disk by $4$ disjoint subdisks (with equal distance to each other) of radius $1/4$ inside and tangent ... More
The Optimal Majority Threshold as a Function of the Variation Coefficient of the EnvironmentJan 21 2018Within the model of social dynamics determined by collective decisions in a stochastic environment (ViSE model), we consider the case of a homogeneous society consisting of classically rational economic agents (or homines economici, or egoists). We present ... More
Joint estimation of parameters in Ising modelJan 19 2018We study joint estimation of the inverse temperature and magnetization parameters $(\beta,B)$ of an Ising model with a non-negative coupling matrix $A_n$ of size $n\times n$, given one sample from the Ising model. We give a general bound on the rate of ... More
Ergodic robust maximization of asymptotic growthJan 19 2018We consider the problem of robustly maximizing the growth rate of investor wealth in the presence of model uncertainty. Possible models are all those under which the assets' region $E$ and instantaneous covariation $c$ are known, and where additionally ... More
Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systemsJan 19 2018We obtain a Central Limit Theorem for the normalized number of real roots of a square Kostlan-Shub-Smale random polynomial system of any size as the degree goes to infinity. A study of the asymptotic variance of the number of roots is needed, this result ... More
Clark representation for self-intersection local times of Gaussian integratorsJan 18 2018In present article we prove the existence of multiple self-intersection local times, describe its Ito-Wiener expansion and establish Clark representation for the class of Gaussian integrators generated by operators with a finite dimensional kernel.
Entrance laws for annihilating Brownian motionsJan 18 2018Consider a system of particles moving independently as Brownian motions until two of them meet, when the colliding pair annihilates instantly. The construction of such a system of annihilating Brownian motions (aBMs) is straightforward as long as we start ... More
Characterization of probability distribution convergence in Wasserstein distance by $L^{p}$-quantization error functionJan 18 2018We establish the condition for probability measure characterization by $L^{p}$-quantization error function in $\mathbb{R}^{d}$. There are two types of characterization: the static characterization for the identity of two probability measures, and the ... More
A Markov Process Approach to the asymptotic Theory of abstract Cauchy Problems driven by Poisson ProcessesJan 17 2018Jan 22 2018In this paper, we employ Markov process theory to prove asymptotic results for a class of stochastic processes which arise as solutions of a stochastic evolution inclusion and are given by the representation formula \begin{align*} \mathbb{X}_{x}(t)=\sum ... More
The rank of random regular digraphs of constant degreeJan 17 2018Let $d$ be a fixed large integer. For any $n$ larger than $d$, let $A_n$ be the adjacency matrix of the random directed $d$-regular graph on $n$ vertices, with the uniform distribution. We show that $A_n$ has rank at least $n-1$ with probability going ... More
Circular law for sparse random regular digraphsJan 17 2018Jan 21 2018Fix a constant $C\geq 1$ and let $d=d(n)$ satisfy $d\leq \ln^{C} n$ for every large integer $n$. Denote by $A_n$ the adjacency matrix of a uniform random directed $d$-regular graph on $n$ vertices. We show that, as long as $d\to\infty$ with $n$, the empirical ... More
Structure of eigenvectors of random regular digraphsJan 17 2018Jan 19 2018Let $n$ be a large integer, let $d$ satisfy $C\leq d\leq \exp(c\sqrt{\ln n})$ for some universal constants $c, C>0$, and let $z\in {\mathcal C}$. Further, denote by $M$ the adjacency matrix of a random $d$-regular directed graph on $n$ vertices. In this ... More
Persistence of one-dimensional AR(1)-sequencesJan 13 2018For a class of one-dimensional autoregressive processes $(X_n)$ we consider the tail behaviour of the stopping time $T_0=\min \lbrace n\geq 1: X_n\leq 0 \rbrace$. We discuss existing general analytical approaches to this and related problems and propose ... More
Boolean functions: noise stability, non-interactive correlation, and mutual informationJan 13 2018Let $\epsilon\in[0, 1/2]$ be the noise parameter and $p>1$. We study the isoperimetric problem that for fixed mean $\E f$ which Boolean function $f$ maximizes the $p$-th moment $\E(T_\epsilon f)^p$ of the noise operator $T_{\epsilon}$ acting on Boolean ... More
Couplings in L^p distance of two Brownian motions and their L{é}vy areaJan 12 2018We study co-adapted couplings of (canonical hypoelliptic) diffu-sions on the (subRiemannian) Heisenberg group, that we call (Heisenberg) Brow-nian motions and are the joint laws of a planar Brownian motion with its L{\'e}vy area. We show that contrary ... More
On notions of Q-independence and Q-identical distributivenessJan 12 2018In a recent article A.M. Kagan and G.J.Sz\'ekely introduced a notion of Q-independent and Q-identical distributed random variables. We give a complete description of polynomials which appear in these definitions.
No eigenvalues outside the limiting support of the spectral distribution of general sample covariance matricesJan 10 2018This paper is to investigate the spectral properties of sample covariance matrices under a more general population. We consider a class of matrices of the form $\mathbf S_n=\frac1n\mathbf B_n\mathbf X_n\mathbf X_n^*\mathbf B_n^*$, where $\mathbf B_n$ ... More
Global fluctuations for 1D log-gas dynamics. (2) Covariance kernel and supportJan 09 2018We consider the hydrodynamic limit in the macroscopic regime of the coupled system of stochastic differential equations, $ d\lambda_t^i=\frac{1}{\sqrt{N}} dW_t^i - V'(\lambda_t^i) dt+ \frac{\beta}{2N} \sum_{j\not=i} \frac{dt}{\lambda^i_t-\lambda^j_t}, ... More
Concatenation and Pasting of Right ProcessesJan 08 2018A universal method for the concatenation of a sequence of Markov right processes is established. It is then applied to the continued pasting of two Markov right processes, which can be used for pathwise constructions of locally defined processes like ... More
Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measuresJan 08 2018We study convergence in variation of probability solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary solutions. We obtain sufficient conditions for the exponential convergence of solutions to the stationary solution in case of coefficients ... More
Covariant Schrödinger semigroups on noncompact Riemannian manifoldsJan 04 2018This monograph develops the theory of covariant Schr\"odinger semigroups acting on sections of vector bundles over noncompact Riemannian manifolds from scratch. Contents: I. Sobolev spaces on vector bundles II. Smooth heat kernels on vector bundles III. ... More
Ergodic BSDE with an unbounded and multiplicative underlying diffusion and application to large time behavior of viscosity solution of HJB equationJan 04 2018In this paper, we study ergodic backward stochastic differential equations (EBSDEs for short), for which the underlying diffusion is assumed to be multiplicative and of at most linear growth. The fact that the forward process has an unbounded diffusion ... More
The distribution of overlaps between eigenvectors of Ginibre matricesJan 04 2018We study the overlaps between eigenvectors of nonnormal matrices. They quantify the stability of the spectrum, and characterize the joint eigenvalues increments under Dyson-type dynamics. Well known work by Chalker and Mehlig calculated the expectation ... More
A new definition of random setsDec 26 2017A new definition of random sets is proposed. It is based on the distance in measurable space and uses negative definite kernels for continuation from initial space to that of random sets. This approach has no connection to Hausdorff distance between sets. ... More
A large-population limit for a Markovian model of group-structured populationsDec 25 2017Dec 28 2017A Markovian model of group-structured (two-level) population dynamics features births, deaths, and migrations of individuals, and fission and extinction of groups. These models are useful for studying group selection and other evolutionary processes that ... More
The Minimal Position of a Stable Branching Random WalkDec 25 2017In this paper, a branching random walk $(V(x))$ in the boundary case is studied, where the associated one dimensional random walk is in the domain of attraction of an $\alpha-$stable law with $1<\alpha<2$. Let $M_n$ be the minimal position of $(V(x))$ ... More
Heat Equation With a Geometric Rough Path Potential in One Space Dimension: Existence and Regularity of SolutionDec 21 2017A solution of the heat equation with a distribution-valued potential is constructed by regularization. When the potential is the generalized derivative of a H\"{o}lder continuous function, regularity of the resulting solution is in line with the standard ... More
Efficient multicut enumeration of k-out-of-n:F and consecutive k-out-of-n:F systemsDec 21 2017We study multiple simultaneous cut events for k-out-of-n:F and linear consecutive k-out-of-n:F systems in which each component has a constant failure probability. We list the multicuts of these systems and describe the structural differences between them. ... More
Local optima of the Sherrington-Kirkpatrick HamiltonianDec 21 2017We study local optima of the Hamiltonian of the Sherrington-Kirkpatrick model. We compute the exponent of the expected number of local optima and determine the "typical" value of the Hamiltonian.
On a generalization of the Dvoretzky-Wald-Wolfowitz theorem with an application to a robust optimization problemDec 20 2017A generalization of the Dvoretzky-Wald-Wolfowitz theorem to the case of conditional expectations is provided assuming that the $\sigma$-field on the state space has no conditional atoms.
Constant curvature metrics for Markov chainsDec 07 2017We consider metrics which are preserved under a $p$-Wasserstein transport map, up to a possible contraction. In the case $p=1$ this corresponds to a metric which is uniformly curved in the sense of coarse Ricci curvature. We investigate the existence ... More
Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: Application to heat transfer in building wallsNov 26 2017In this work, we present the ensemble-marginalized Kalman filter (EnMKF), a sequential algorithm analogous to our previously proposed approach [1,2], for estimating the state and parameters of linear parabolic partial differential equations in initial-boundary ... More
Pinned diffusions and Markov bridgesNov 23 2017In this article we consider a family of real-valued diffusion processes on the time interval $[0,1]$ indexed by their prescribed initial value $x \in \mathbb{R}$ and another point in space, $y \in \mathbb{R}$. We first present an easy-to-check condition ... More
Random affine simplexesNov 17 2017For a fixed $k\in\{1,\dots,d\}$ consider random vectors $X_0,\dots, X_{k}\in\mathbb R^d$ with an arbitrary spherically symmetric joint density function. Let $A$ be any non-singular $d\times d$ matrix. We show that the $k$-dimensional volume of the convex ... More
Derivation of the stochastic Burgers equation with Dirichlet boundary conditions from the WASEPOct 30 2017We consider the weakly asymmetric simple exclusion process on the discrete space $\{1,...,n-1\}$, in contact with stochastic reservoirs, both with density $\rho\in{(0,1)}$ at the extremity points, and starting from the invariant state, namely the Bernoulli ... More
Central limit theorem for the free energy of the random field Ising modelOct 24 2017A central limit theorem is proved for the free energy of the random field Ising model with all plus or all minus boundary condition, at any temperature (including zero temperature) and any dimension. This solves a problem posed by Wehr and Aizenman in ... More
Building your path to escape from homeSep 29 2017Random walks on dynamic graphs have received increasingly more attention over the last decade from different academic communities. Despite the relatively large literature very little is known about random walks that construct the graph where they walk ... More
Equilibrium distributions and discrete Schur-constant modelsSep 28 2017This paper introduces Schur-constant equilibrium distribution models of dimension n for arithmetic non-negative random variables. Such a model is defined through the (several orders) equilibrium distributions of a univariate survival function. First, ... More
Equilibrium fluctuations for the weakly asymmetric discrete Atlas modelSep 20 2017This contribution aims at presenting and generalizing a recent work of Hernandez, Jara and Valentim [DOI:10.1016/]. We consider the weakly asymmetric version of the so-called discrete Atlas model, which has been introduced there. Precisely, ... More
Area anomaly and generalized drift of iterated sums for hidden Markov walksSep 13 2017Following our previous results on Markov chains on periodic graphs, we study the convergence in rough path topology of a certain class of discrete processes, the hidden Markov walks, to a Brownian motion with an area anomaly. This area anomaly, which ... More
On the decay of correlations in the random field Ising modelSep 13 2017Nov 30 2017In a celebrated 1990 paper, Aizenman and Wehr proved that the two-dimensional random field Ising model has a unique infinite volume Gibbs state at any temperature. The proof is ergodic-theoretic in nature and does not provide any quantitative information. ... More
Non-Gaussian limit of a tracer motion in an incompressible flowSep 12 2017We consider a massless tracer particle moving in a random, stationary, isotropic and divergence free velocity field. We identify a class of fields, for which the limit of the laws of appropriately scaled tracer trajectory processes is non-Gaussian but ... More
Estimating graph parameters via random walks with restartsSep 04 2017In this paper we discuss the problem of estimating graph parameters from a random walk with restarts at a fixed vertex $x$. For regular graphs $G$, one can estimate the number of vertices $n_G$ and the $\ell^2$ mixing time of $G$ from $x$ in $\widetilde{O}(\sqrt{n_G}\,(t_{\rm ... More
GALILEO: A Generalized Low-Entropy Mixture ModelAug 24 2017We present a new method of generating mixture models for data with categorical attributes. The keys to this approach are an entropy-based density metric in categorical space and annealing of high-entropy/low-density components from an initial state with ... More