Related papers: Universality of the minimum modulus for random tri…
We consider finite point subsets (distributions) in compact metric spaces. Non-trivial bounds for sums of distances between points of distributions and for discrepancies of distributions in metric balls are given in the case of general…
We study the distribution of the least singular value associated to an ensemble of sparse random matrices. Our motivating example is the ensemble of $N\times N$ matrices whose entries are chosen independently from a Bernoulli distribution…
This article investigates the behavior of the continuous-time simple random walk on $\mathbb{Z}^d$, $d \geq 3$. We derive an asymptotic lower bound on the principal exponential rate of decay for the probability that the average value over a…
We prove that in the limit of large dimension, the distribution of the logarithm of the characteristic polynomial of a generalized Wigner matrix converges to a log-correlated field. In particular, this shows that the limiting joint…
The universality of the directed polymer model and the analogous KPZ equation is supported by numerical simulations using non-Gaussian random probability distributions in two, three and four dimensions. It is shown that although in the…
In this paper we consider uniformly random lozenge tilings of arbitrary domains approximating (after suitable normalization) a closed, simply-connected subset of $\mathbb{R}^2$ with piecewise smooth, simple boundary. We show that the local…
In this work we establish a link between two different phenomena that were studied in a large and growing number of biological, composite and soft media: the diffusion in compartmentalized environment and the Brownian yet non-Gaussian…
In this paper we discuss general tridiagonal matrix models which are natural extensions of the ones given by Dumitriu and Edelman. We prove here the convergence of the distribution of the eigenvalues and compute the limiting distributions…
We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with Hermitian matrices whose elements perform a random walk in the space of complex numbers, satisfy certain partial…
We identify the scaling region of a width O(n^{-1}) in the vicinity of the accumulation points $t=\pm 1$ of the real roots of a random Kac-like polynomial of large degree n. We argue that the density of the real roots in this region tends…
The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous-time random walks with exponential and heavy-tailed waiting time distributions. The space dependent variable-order…
We obtain new bounds on complete rational exponential sums with sparse polynomials modulo a prime, under some mild conditions on the degrees of the monomials of such polynomials. These bounds, when they apply, give explicit versions of a…
We consider $(1+1)$-dimensional directed polymers in a random potential and provide sufficient conditions guaranteeing joint localization. Joint localization means that for typical realizations of the environment, and for polymers started…
The distribution of the modulus of the extreme eigenvalues is investigated for the complex Ginibre and complex induced Ginibre ensembles in the limit of large dimensions of random matrices. The limiting distribution of the scaled spectral…
The aim of this paper is to give a precise asymptotic description of some eigenvalue statistics stemming from random matrix theory. More precisely, we consider random determinants of the GUE, Laguerre, Uniform Gram and Jacobi beta ensembles…
We obtain uniform asymptotics for polynomials orthogonal on a fixed and varying arc of the unit circle with a positive analytic weight function. We also complete the proof of the large $s$ asymptotic expansion for the Fredholm determinant…
We prove that random walks on a family of tilings of d-dimensional Euclidean space, with a canonical choice of conductances, converge to Brownian motion modulo time parameterization. This class of tilings includes Delaunay triangulations…
In this article, universal concentration estimates are established for the local times of random walks on weighted graphs in terms of the resistance metric. As a particular application of these, a modulus of continuity for local times is…
We study an extended dynamical system on the non-negative real line with piecewise linear non-uniformly expanding local dynamics. With a uniformly distributed initial state, the distribution of successive states coincides with that of a…
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…