Related papers: Compound Poisson statistics in conventional and no…
Introduced in the late 1960's, the asymmetric exclusion process (ASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites with…
The analysis of count data is commonly done using Poisson models. Negative binomial models are a straightforward and readily motivated generalization for the case of overdispersed data, i.e., when the observed variance is greater than…
We derive large-sample and other limiting distributions of the ``frequency of frequencies'' vector, ${\bf M_n}$, together with the number of species, $K_n$, in a Poisson-Dirichlet or generalised Poisson-Dirichlet gene or species sampling…
In this paper, we study the averaging principle and central limit theorem for multi-scale stochastic differential equations with state-dependent switching. To accomplish this, we first study the Poisson equation associated with a Markov…
We study the length of cycles of random permutations drawn from the Mallows distribution. Under this distribution, the probability of a permutation $\pi \in \mathbb{S}_n$ is proportional to $q^{\textrm{inv}(\pi)}$ where $0<q\le 1$ and…
The limiting distribution of the normalized number of comparisons used by Quicksort to sort an array of n numbers is known to be the unique fixed point with zero mean of a certain distributional transformation S. We study the convergence to…
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…
In this paper, we study stochastic ordering results between two finite mixtures with single and multiple outliers, assuming subpopulations follow general exponentiated location-scale distributions. For single-outlier mixtures, several…
We study how the order of N independent random walks in one dimension evolves with time. Our focus is statistical properties of the inversion number m, defined as the number of pairs that are out of sort with respect to the initial…
Let $A$ be a compact $d$-dimensional $C^2$ Riemannian manifold with boundary, embedded in ${\bf R}^m$ where $m \geq d \geq 2$, and let $B$ be a nice subset of $A$ (possibly $B=A$). Let $X_1,X_2, \ldots $ be independent random uniform points…
Denoting by Sigma(S) the set of subset sums of a subset S of a finite abelian group G, we prove that |Sigma(S)| >= |S|(|S|+2)/4-1 whenever S is symmetric, |G| is odd and Sigma(S) is aperiodic. Up to an additive constant of 2 this result is…
We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…
In this article, we prove the cutoff phenomenon for a general class of the discrete-time nonlinear recombination models. This system models the evolution of a probability measure on a finite product space $S^n$ representing the state of…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
Let $A$ be a set of natural numbers. Recent work has suggested a strong link between the additive energy of $A$ (the number of solutions to $a_1 + a_2 = a_3 + a_4$ with $a_i \in A$) and the metric Poissonian property, which is a fine-scale…
Kipnis and Varadhan showed that for an additive functional, $S_n$ say, of a reversible Markov chain the condition $E(S_n^{2})/n \to \kappa \in (0,\infty)$ implies the convergence of the conditional distribution of $S_n/\sqrt{E(S_n^{2}})$,…
We show that for systems that allow a Young tower construction with polynomially decaying correlations the return times to metric balls are in the limit Poisson distributed. We also provide error terms which are powers of logarithm of the…
This paper is concerned with the study of the random variable $K_n$ denoting the number of distinct elements in a random sample $(X_1, \dots, X_n)$ of exchangeable random variables driven by the two parameter Poisson-Dirichlet distribution,…