Related papers: Multivariate limit theorems in the context of long…
We consider a class of Gaussian Free Fields denoted by $(g_x)_{x \in {\cal V}_N}$, where $ {\cal V}_N = \{0,1\}^N$ and $N\in \mathbb{Z}_+$. These fields are related to a general class of $N$-dimensional random walks on the hypercube, which…
In this paper, we discuss the convergence rate of empirical processes of Gaussian processes for a large class of function families. Our main goal is to show that the tail of the uniform norm of the empirical processes can be dominated by…
The paper proves several limit theorems for linear eigenvalue statistics of overlapping Wigner and sample covariance matrices. It is shown that the covariance of the limiting multivariate Gaussian distribution is diagonalized by choosing…
We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general…
In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…
We consider the setting where a collection of time series, modeled as random processes, evolve in a causal manner, and one is interested in learning the graph governing the relationships of these processes. A special case of wide interest…
There are many notions of rank in multilinear algebra: tensor rank, partition rank, slice rank, and strength (or Schmidt rank) are a few examples. Typically the rank $\le r$ locus is not Zariski closed, and understanding the closure (the…
Hermite processes are a class of self-similar processes with stationary increments. They often arise in limit theorems under long-range dependence. We derive new representations of Hermite processes with multiple Wiener-It\^o integrals,…
In this paper, we explore the connection between convergence in distribution and Mallows distance in the context of positively associated random variables. Our results extend some known invariance principles for sequences with FKG property.…
Bessel processes $(X_{t,k})_{t\ge0}$ in $N$ dimensions are classified via associated root systems and multiplicity constants $k\ge0$. They describe interacting Calogero-Moser-Suther\-land particle systems with $N$ particles and are related…
We analyse large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time t depends itself on the value q_t of the time-averaged quantity. First we consider the elephant random walk…
This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following Doukhan and Louhichi (1999), we measure the strength of dependence by covariances of nonlinearly…
We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices. This random walk, already known to be transient, has different horizontal and vertical fluctuations leading to…
Motivated by the study of asymptotic behaviour of the bandit problems, we obtain several strategy-driven limit theorems including the law of large numbers, the large deviation principle, and the central limit theorem. Different from the…
The aim of the present article is to establish the connection between the existence of the limit along the normal and an admissible limit at a fixed boundary point for holomorphic functions of several complex variables.
Consider a sequence of polynomials of bounded degree evaluated in independent Gaussian, Gamma or Beta random variables. We show that, if this sequence converges in law to a nonconstant distribution, then (i) the limit distribution is…
Ordinal pattern dependence is a multivariate dependence measure based on the co-movement of two time series. In strong connection to ordinal time series analysis, the ordinal information is taken into account to derive robust results on the…
We show that the central limit theorem for linear statistics over determinantal point processes with $J$-Hermitian kernels holds under fairly general conditions. In particular, We establish Gaussian limit for linear statistics over…
We study distributions of random vectors whose components are second order polynomials in Gaussian random variables. Assuming that the law of such a vector is not absolutely continuous with respect to Lebesgue measure, we derive some…
We provide an abstract multivariate central limit theorem with the Lindeberg-type error bounded in terms of Lipschitz functions (Wasserstein 1-distance) or functions with bounded second or third derivatives. The result is proved by means of…