Inspired by a concept in comparative genomics, we investigate properties of randomly chosen members of G1(m,n,t), the set of bipartite graphs with m left vertices, n right vertices, t edges, and each vertex of degree at least one. We give asymptotic results for the number of such graphs and the...

We study the occupation measure of various sets for a symmetric transient random walk in Zd with finite variances. Let denote the occupation time of the set A up to time n. It is shown that tends to a finite limit as n--[infinity]. The limit is expressed in terms of the largest eigenvalue of a...

In this article, superpositions of possibly dependent point processes on a general space are considered. Using Stein's method for Poisson process approximation, an estimate is given for the Wasserstein distance d2 between the distribution of such a superposition and an appropriate Poisson...

We establish the moderate deviation principle (MDP) for the family ofwhere 0[kappa]0.5 and are slow and fast diffusion processes. We embed the original problem in the MDP study for the pair . The main tool for the MDP analysis is the Poisson equation technique, borrowed from the recent papers of...

Let L be a multidimensional Lévy process under P in its own filtration and consider all probability measures Q turning L into a local martingale. The minimal entropy martingale measure QE is the unique Q which minimizes the relative entropy with respect to P. We prove that L is still a Lévy...

Logarithmic Sobolev inequalities are a well-studied technique for estimating rates of convergence of Markov chains to their stationary distributions. In contrast to continuous state spaces, discrete settings admit several distinct log Sobolev inequalities, one of which is the subject of this...

By adapting the renormalization techniques of Pisztora (Probab. Theory Relat. Fields 104 (1996) 427), we establish surface order large deviations estimates for FK-percolation on with parameter q[greater-or-equal, slanted]1 and for the corresponding Potts models. Our results are valid up to the...

The serial harnesses introduced by Hammersley describe the motion of a hypersurface of dimension d embedded in a space of dimension d+1. The height assigned to each site i of is updated by taking a weighted average of the heights of some of the neighbors of i plus a "noise" (a centered random...

We establish a representation formula for the transition probability density of a diffusion perturbed by a vector field, which takes a form of Cameron-Martin's formula for pinned diffusions. As an application, by carefully estimating the mixed moments of a Gaussian process, we deduce explicit,...

For symmetric stable processes with negative drift and continuous or discrete time the probabilistic tails of the subadditive functionals, acting on sample paths, are investigated. We prove a general result and applying it to examples show how the rate of decay can vary. The proof is based on...