Related papers: Poisson--Dirichlet Limit Theorems in Combinatorial…

We study mean-field inclusion processes with an additional slow phase, in which particle interactions occur at a vanishing rate proportional to the inverse system size. In the thermodynamic limit, such systems exhibit condensation at high…

Flexible bandwidth needlets provide a localized multiscale framework with scale-adaptive frequency resolution, enabling effective analysis of spherical Poisson random fields exhibiting spatial inhomogeneity and scale variation. We establish…

We introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The…

A regenerative random composition of integer $n$ is constructed by allocating $n$ standard exponential points over a countable number of intervals, comprising the complement of the closed range of a subordinator $S$. Assuming that the…

In this article, we study a model of random permutations, which we call random standardized permutations, based on a sequence of i.i.d. random variables. This model generalizes others, such as the riffle-shuffle and the major-index-biased…

How much dependence is there in the prime factorization of a random integer distributed uniformly from 1 to n? How much dependence is there in the decomposition into cycles of a random permutation of n points? What is the relation between…

We find a sharp combinatorial bound for the metric entropy of sets in R^n and general classes of functions. This solves two basic combinatorial conjectures on the empirical processes. 1. A class of functions satisfies the uniform Central…

Let $ V_{n} = X_{1,n} + X_{2,n} + \cdots + X_{n,n}$ where $X_{i,n}$ are Bernoulli random variables which take the value $1$ with probability $b(i;n)$. Let $\lambda_{n} = \sum\limits_{i=1}^{n} b(i;n) $, $\lambda = \lim\limits_{n \to \infty}…

Any limiting point process for the time normalized exceedances of high levels by a stationary sequence is necessarily compound Poisson under appropriate long range dependence conditions. Typically exceedances appear in clusters. The…

We derive new bounds of the remainder in a combinatorial central limit theorem without assumptions on independence and existence of moments of summands. For independent random variables our theorems imply Esseen and Berry-Esseen type…

In this note we discuss additional properties of mixed Poisson distributions. We discuss the convergence of mixed Poisson distributions to its mixing distribution for the scaling parameter tending to infinity. Moreover, we obtain a central…

We consider stopping criteria that balance algebraic and discretization errors for the conjugate gradient algorithm applied to high-order finite element discretizations of Poisson problems. Firstly, we introduce a new stopping criterion…

In this article we survey properties of mixed Poisson distributions and probabilistic aspects of the Stirling transform: given a non-negative random variable $X$ with moment sequence $(\mu_s)_{s\in\mathbb{N}}$ we determine a discrete random…

We prove the Central Limit Theorem and superpolynomial mixing for environment viewed for the particle process in quasi periodic Diophantine random environment. The main ingredients are smoothness estimates for the solution of the Poisson…

The purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic dynamics developed by the first author \textit{et al}. to establish quenched versions of the large deviation…

We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the…

Given a periodic point $\omega$ in a $\psi$-mixing shift with countable alphabet, the sequence $\{S_{n}\}$ of random variables counting the number of multiple returns to shrinking cylindrical neighborhoods of $\omega$ is considered.…

We study random composite structures considered up to symmetry that are sampled according to weights on the inner and outer structures. This model may be viewed as an unlabelled version of Gibbs partitions and encompasses multisets of…

Let $x \ge 2$, let $N_x$ be an integer chosen uniformly at random from the set $\mathbb Z \cap [1, x]$, and let $(V_1, V_2, \ldots)$ be a Poisson--Dirichlet process of parameter $1$. We prove that there exists a coupling of these two random…

We prove a Poisson limit theorem in the total variation distance of functionals of a general Poisson point process using the Malliavin-Stein method. Our estimates only involve first and second order difference operators and are closely…