Related papers: Integer Partitions and Exclusion Statistics

We provide a general result for bounding the difference between point probabilities of integer supported distributions and the translated Poisson distribution, a convenient alternative to the discretized normal. We illustrate our theorem in…

For a class of Gaussian stationary processes, we prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly growing linear boundary. The limit is a double exponential (Gumbel) distribution.

For $G=G_{n, 1/2}$, the Erd\H{o}s--Renyi random graph, let $X_n$ be the random variable representing the number of distinct partitions of $V(G)$ into sets $A_1, \ldots, A_q$ so that the degree of each vertex in $G[A_i]$ is divisible by $q$…

The purpose of this paper is to estimate the intensity of some random measure by a piecewise constant function on a finite partition of the underlying measurable space. Given a (possibly large) family of candidate partitions, we build a…

Let X be a second countable locally compact Abelian group. Let $\xi_1, \xi_2$ be independent random variables with values in the group X and distributions $\mu_1, \mu_2$ such that the sum $\xi_1+\xi_2$ and the difference $\xi_1-\xi_2$ are…

Extending the rigorous presentation of the classical umbral calculus given by Rota and Taylor in 1994, the so-called partition polynomials are interpreted with the aim to point out the umbral nature of the Poisson random variables. Among…

This paper proposes groove-like potential structures for the observation of quantum information processing by trapped particles. As an illustration the effect of quantum statistics at a 50-50 beam splitter is investigated. For…

In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…

The class of minimal difference partitions MDP($q$) (with gap $q$) is defined by the condition that successive parts in an integer partition differ from one another by at least $q\ge 0$. In a recent series of papers by A. Comtet and…

We consider the asymptotic distribution of a cell in a 2 x ... x 2 contingency table as the fixed marginal totals tend to infinity. The asymptotic order of the cell variance is derived and a useful diagnostic is given for determining…

The minimal excludant of a partition $\lambda$, $\rm{mex}(\lambda)$, is the smallest positive integer that is not a part of $\lambda$. For a positive integer $n$, $ \sigma\, \rm{mex}(n)$ denotes the sum of the minimal excludants of all…

In this paper, we show that the methods of mathematical statistical physics can be successfully applied to random fields in finite volumes. As a result, we obtain simple necessary and sufficient conditions for the existence and uniqueness…

This article provides some characterizations of extended COM-Poisson distribution: conditional distribution given the sum, functional operator characterization (Stein identity). We also give some conditions such that the extended…

By exploiting the well-known observation that size-biasing or zero-biasing an infinitely divisible random variable may be achieved by adding an independent increment, combined with tools from Stein's method for compound Poisson and Gaussian…

We propose a probability distribution for multivariate binary random variables. The probability distribution is expressed as principal minors of the parameter matrix, which is a matrix analogous to the inverse covariance matrix in the…

In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on the mathematical study of statistical systems. Central…

We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator…

Motivated by Haldane's exclusion statistics, we construct creation and annihilation operators for $g$-ons using a bosonic algebra. We find that $g$-ons appear due to the breaking of a descrete symmetry of the original bosonic system. This…

The investigation of partitions of integers plays an important role in combinatorics and number theory. Among the many variations, partitions into powers $0<\alpha<1$ were of recent interest. In the present paper we want to extend our…

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…