Related papers: Limiting behaviour of pattern counts in biased bin…

Renyi's "thinning" operation on a discrete random variable is a natural discrete analog of the scaling operation for continuous random variables. The properties of thinning are investigated in an information-theoretic context, especially in…

We study measures on random partitions, arising from condensing stochastic particle systems with stationary product distributions. We provide fairly general conditions on the stationary weights, which lead to Poisson-Dirichlet statistics of…

We generalize the Poisson limit theorem to binary functions of random objects whose law is invariant under the action of an amenable group. Examples include stationary random fields, exchangeable sequences, and exchangeable graphs. A…

Berry Esseen type bounds to the normal, based on zero- and size-bias couplings, are derived using Stein's method. The zero biasing bounds are illustrated with an application to combinatorial central limit theorems where the random…

For branching processes, the generating functions for limit distributions of so-called ratios of probabilities of rare events satisfy the Schr\"oder-type integral-functional equations. Excepting limited special cases, the corresponding…

For the trace of Besov spaces $B^s_{p,q}$ onto a hyperplane, the borderline case with $s=\frac{n}{p}-(n-1)$ and $0<p<1$ is analysed and a new dependence on the sum-exponent $q$ is found. Through examples the restriction operator defined for…

A permutation sequence $(\sigma_n)_{n \in \mathbb{N}}$ is said to be convergent if, for every fixed permutation $\tau$, the density of occurrences of $\tau$ in the elements of the sequence converges. We prove that such a convergent sequence…

A nonparametric variant of the Kiefer--Weiss problem is proposed and investigated. In analogy to the classical Kiefer--Weiss problem, the objective is to minimize the maximum expected sample size of a sequential test. However, instead of…

Years ago, Zeev Rudnick defined the Poisson generic real numbers by counting the number of occurrences of long blocks of digits in the initial segments of the expansions of the real numbers in a fixed integer base. Peres and Weiss proved…

We propose a way to remove the bias of a Poisson regression when the subjects are partially observed. In this paper we address this issue under certain assumptions about the missing-data generating process. We fix the total number of…

We study the notion of sparseness for regular languages over finite trees and infinite words. A language of trees is called sparse if the relative number of $n$-node trees in the language tends to zero, and a language of infinite words is…

Subsets of F_2^n that are eps-biased, meaning that the parity of any set of bits is even or odd with probability eps close to 1/2, are powerful tools for derandomization. A simple randomized construction shows that such sets exist of size…

This paper describes performance bounds for compressed sensing in the presence of Poisson noise when the underlying signal, a vector of Poisson intensities, is sparse or compressible (admits a sparse approximation). The signal-independent…

The purpose of this article is to present a general method to find limiting laws for some renormalized statistics on random permutations. The model considered here is Ewens sampling model, which generalizes uniform random permutations. We…

We show that the Conway--Maxwell--Poisson distribution can be arbitrarily underdispersed when parametrized via its mean. More precisely, if the mean $\mu$ is an integer then the limiting distribution is a unit probability mass at $\mu$. If…

This work is concern with testing the low-dimensional parameters of interest with divergent dimensional data and variable selection for the rest under the sparse case. A consistent test via the partial penalized likelihood approach, called…

Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the…

We prove limit theorems for the number of fixed points occurring in a random pattern-avoiding permutation distributed according to a one-parameter family of biased distributions. The bias parameter exponentially tilts the distribution…

Consider a random permutation of $\{1, \ldots, \lfloor n^{t_2}\rfloor\}$ drawn according to the Ewens measure with parameter $t_1$ and let $K(n, t)$ denote the number of its cycles, where $t\equiv (t_1, t_2)\in\mathbb [0, 1]^2$. Next,…

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…