Related papers: Processes with block-associated increments
We investigate the two-points correlation function for several boundary-driven interacting particle systems. Our goal is to show that the time evolution of that correlation function is solution to a partial differential equation that can be…
Consider a one dimensional simple random walk $X=(X_n)_{n\geq0}$. We form a new simple symmetric random walk $Y=(Y_n)_{n\geq0}$ by taking sums of products of the increments of $X$ and study the two-dimensional walk…
Multivariate (or vector-valued) processes are important for modeling multiple variables. The fractal indices of the components of the underlying multivariate process play a key role in characterizing the dependence structures and…
The concept of entropy connects the number of possible configurations with the number of variables in large stochastic systems. Independent or weakly interacting variables render the number of configurations scale exponentially with the…
We consider the joint distribution of eigenvalue clusters of the Wigner ensemble separated by macroscopic distances (i.e., on the same scale as the difference between the edges of the semicircle law). We prove that under an averaging…
An extension of the latent class model is presented for clustering categorical data by relaxing the classical "class conditional independence assumption" of variables. This model consists in grouping the variables into inter-independent and…
Our interest is in the scaled joint distribution associated with $k$-increasing subsequences for random involutions with a prescribed number of fixed points. We proceed by specifying in terms of correlation functions the same distribution…
In the last decade there has been increasing interest in the fields of random matrices, interacting particle systems, stochastic growth models, and the connections between these areas. For instance, several objects appearing in the limit of…
A formalism using a double Laplace Fourier transform of the transport equation yields the return probabilities of the vacancy in the vicinity of the tracer atom in the presence of solute-vacancy interactions of arbitrary extension. Studying…
Mixing rates and decay of correlations for dynamics defined by potentials with summable variations are well understood, but little is known for non-summable variations. In this paper, we exhibit upper bounds for these quantities in the case…
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…
The maximal correlation coefficient is a well-established generalization of the Pearson correlation coefficient for measuring non-linear dependence between random variables. It is appealing from a theoretical standpoint, satisfying…
In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…
In this paper, we introduce the notion of a ``pairwise independent correlation gap'' for set functions with random elements. The pairwise independent correlation gap is defined as the ratio of the maximum expected value of a set function…
We establish a connection between dependence structures and subclasses of distortion riskmetrics under which the latter are additive. A new notion of positive dependence, called partial comonotonicity, is developed, which nests the existing…
The analysis of the entanglement entropy of a subsystem of a one-dimensional quantum system is a powerful tool for unravelling its critical nature. For instance, the scaling behaviour of the entanglement entropy determines the central…
Cohen and Kontorovich (COLT 2023) initiated the study of what we call here the Binomial Empirical Process: the maximal absolute value of a sequence of inhomogeneous normalized and centered binomials. They almost fully analyzed the case…
In a recent paper [2] the author introduced and investigated a random walk model similar to a model introduced in [1]. In these models the increment of the random walk depends on the complete past of the process. In this note I will point…
The block entanglement entropy and fluctuations are investigated in one dimension in finite size correlated electron systems using the Gutzwiller wave function as a prototype correlated electron state. Entanglement entropy shows logarithmic…
The problem of combining p-values is an old and fundamental one, and the classic assumption of independence is often violated or unverifiable in many applications. There are many well-known rules that can combine a set of arbitrarily…