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Construct a random set by independently selecting each finite subset of the integers with some probability depending on the set up to translations and taking the union of the selected sets. We show that when the only sets selected with…

Probability · Mathematics 2025-06-06 Yinon Spinka

Carlitz [2] initiated a study on degenerate versions of Bernoulli and Euler numbers which has been extended recently to the researches on various degenerate versions of quite a few special numbers and polynomials. They have been explored by…

Number Theory · Mathematics 2021-06-28 Taekyun Kim , Dae san Kim , Hyunseok Lee , Seong Ho Park , Jongkyum Kwon

This paper investigates the theoretical and empirical performance of Fisher-Pitman-type permutation tests for assessing the equality of unknown Poisson mixture distributions. Building on nonparametric maximum likelihood estimators (NPMLEs)…

Methodology · Statistics 2021-06-08 Zhen Miao , Weihao Kong , Ramya Korlakai Vinayak , Wei Sun , Fang Han

We consider the Robinson-Schensted-Knuth algorithm applied to a random input and investigate the shape of the bumping route (in the vicinity of the $y$-axis) when a specified number is inserted into a large Plancherel-distributed tableau.…

Combinatorics · Mathematics 2021-12-06 Łukasz Maślanka , Mikołaj Marciniak , Piotr Śniady

Consider the random quadratic form $T_n=\sum_{1 \leq u < v \leq n} a_{uv} X_u X_v$, where $((a_{uv}))_{1 \leq u, v \leq n}$ is a $\{0, 1\}$-valued symmetric matrix with zeros on the diagonal, and $X_1,$ $X_2, \ldots, X_n$ are i.i.d.…

Probability · Mathematics 2019-12-30 Bhaswar B. Bhattacharya , Somabha Mukherjee , Sumit Mukherjee

The irreducible decomposition of successive restriction and induction of irreducible representations of a symmetric group gives rise to a Markov chain on Young diagrams keeping the Plancherel measure invariant. Starting from this Res-Ind…

Probability · Mathematics 2019-06-25 Akihito Hora

Poisson-like behavior for event count data is ubiquitous in nature. At the same time, differencing of such counts arises in the course of data processing in a variety of areas of application. As a result, the Skellam distribution -- defined…

Probability · Mathematics 2018-04-04 H. L. Gan , Eric D. Kolaczyk

We propose in this paper a random intercept Poisson model in which the random effect distribution is assumed to follow a generalized log-gamma (GLG) distribution. We derive the first two moments for the marginal distribution as well as the…

Methodology · Statistics 2011-05-12 Lizandra C. Fabio , Gilberto A. Paula , Mario de Castro

By the method of Poissonization we confirm some existing results concerning consistent estimation of the structural distribution function in the situation of a large number of rare events. Inconsistency of the so called natural estimator is…

Statistics Theory · Mathematics 2007-06-13 Bert van Es , Stamatis Kolios

We analyze a class of spatial random spanning trees built on a realization of a homogeneous Poisson point process of the plane. This tree has a simple radial structure with the origin as its root. We first use stochastic geometry arguments…

Probability · Mathematics 2007-05-23 Francois Baccelli , Charles Bordenave

In this article, we obtain, for the total variance distance, the error bounds between Poisson and convolution of power series distributions via Stein's method. This provides a unified approach to many known discrete distributions. Several…

Probability · Mathematics 2020-06-26 A. N. Kumar , P. Vellaisamy , F. Viens

Poisson processes and one-dimensional Poisson point processes satisfy three main properties: superposition, thinning, and conditioning. The proof of the first two relies on basic estimates involving the Poisson distribution that are also…

Probability · Mathematics 2025-09-01 Nicolas Lanchier

In the analysis of large random wireless networks, the underlying node distribution is almost ubiquitously assumed to be the homogeneous Poisson point process. In this paper, the node locations are assumed to form a Poisson clustered…

Information Theory · Computer Science 2010-10-11 RadhaKrishna Ganti , Martin Haenggi

We establish a complete picture of condensation in the inclusion process in the thermodynamic limit with vanishing diffusion, covering all scaling regimes of the diffusion parameter and including large deviation results for the maximum…

Probability · Mathematics 2021-07-21 Watthanan Jatuviriyapornchai , Paul Chleboun , Stefan Grosskinsky

Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…

Methodology · Statistics 2025-03-20 Indranil Ghosh , Mina Norouzirad , Filipe J. Marques

In these expository notes, we describe some features of the multiplicative coalescent and its connection with random graphs and minimum spanning trees. We use Pitman's proof of Cayley's formula, which proceeds via a calculation of the…

Probability · Mathematics 2014-08-01 Louigi Addario-Berry

Suppose that a compound Poisson process is observed discretely in time and assume that its jump distribution is supported on the set of natural numbers. In this paper we propose a non-parametric Bayesian approach to estimate the intensity…

Statistics Theory · Mathematics 2020-05-21 Shota Gugushvili , Ester Mariucci , Frank van der Meulen

We show that the chaos representation of some Compound Poisson Type processes displays an underlying intrinsic combinatorial structure, partly independent of the chosen process. From the computational viewpoint, we solve the arising…

Probability · Mathematics 2016-11-08 L. Dello Schiavo

We consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system. This continuous time evolution is interspersed by discrete events that occur at random times and change (reset)…

Systems and Control · Computer Science 2017-11-15 Mohammad Soltani , Abhyudai Singh

Consider a stationary renewal point process on the real line and divide each of the segments it defines in a proportion given by \iid realisations of a fixed distribution $G$ supported by [0,1]. We ask ourselves for which interpoint…

Probability · Mathematics 2014-08-12 Anton Muratov , Sergei Zuyev