Related papers: When Is the Conway-Maxwell-Poisson Distribution In…
We consider the following statistical problem: based on an i.i.d.sample of size n of integer valued random variables with common law m, is it possible to test whether or not the support of m is finite as n goes to infinity? This question is…
Strong negative dependence properties have recently been proved for the symmetric exclusion process. In this paper, we apply these results to prove convergence to the Poisson and normal distributions for various functionals of the process.
The paper deals with studying a connection of the Littlewood--Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions.
In this paper, we study a class of multiscale McKean-Vlasov stochastic systems where the entire system depends on the distribution of the fast component. First of all, by the Poisson equation method we prove that the slow component…
In this study we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson-Cowan equation can be obtained as the limit in probability on compacts for a sequence of microscopic models when the number…
Majorization is a fundamental model of uncertainty with several applications in areas ranging from thermodynamics to entanglement theory, and constitutes one of the pillars of the resource-theoretic approach to physics. Here, we improve on…
We show that if an essentially arbitrary sequence supported on an interval containing $x$ integers, is convolved with a tiny Siegel-Walfisz-type sequence supported on an interval containing $\exp((\log x)^{\varepsilon})$ integers then the…
An exchangeable random matrix is a random matrix with distribution invariant under any permutation of the entries. For such random matrices, we show, as the dimension tends to infinity, that the empirical spectral distribution tends to the…
We consider Gibbs distributions on finite random plane trees with bounded branching. We show that as the order of the tree grows to infinity, the distribution of any finite neighborhood of the root of the tree converges to a limit. We…
We study the probability distribution of the number of zeros of multivariable polynomials with bounded degree over a finite field. We find the probability generating function for each set of bounded degree polynomials. In particular, in the…
We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…
We introduce a probability distribution Q on the group of permutations of the set Z of integers. Distribution Q is a natural extension of the Mallows distribution on the finite symmetric group. A one-sided infinite counterpart of Q,…
In this paper we develop tools for studying limit theorems by means of convexity. We establish bounds for the discrepancy in total variation between probability measures $\mu$ and $\nu$ such that $\nu$ is log-concave with respect to $\mu$.…
We give necessary and sufficient conditions to characterize the convergence in distribution of a sequence of arbitrary random variables to a probability distribution which is the invariant measure of a diffusion process. This class of…
We prove distributional limit theorems for the length of the largest convex minorant of a one-dimensional random walk with independent identically distributed increments. Depending on the increment law, there are several regimes with…
This paper gives a complete characterization of infinitely divisible semimartingales, i.e., semimartingales whose finite dimensional distributions are infinitely divisible. An explicit and essentially unique decomposition of such…
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…
We consider an indecomposable Galton-Watson branching process with countably infinitely many types. Assuming that the process is critical and allowing for infinite variance of the offspring sizes of some (or all) types of particles we…
We propose a flexible model for count time series which has potential uses for both underdispersed and overdispersed data. The model is based on the Conway-Maxwell-Poisson (COM-Poisson) distribution with parameters varying along time to…
In this article, we define a matrix multinomial distribution. We prove some properties of the matrix multinomial distribution. We prove that the matrix Poisson distribution can be used as an approximation to the matrix multinomial…