We study a natural dependent percolation model introduced by Häggström. Consider subcritical Bernoulli bond percolation with a fixed parameter ppc. We define a dependent site percolation model by the following procedure: for each bond cluster, we colour all vertices in the cluster black with...

We consider the free boundary condition Gibbs measure of the Potts model on a random tree. We provide an explicit temperature interval below the ferromagnetic transition temperature for which this measure is extremal, improving older bounds of Mossel and Peres. In information theoretic language...

We consider a branching system consisting of particles moving according to a Markov family in and undergoing subcritical branching with a constant rate V0. New particles immigrate to the system according to a homogeneous space-time Poisson random field. The process of the fluctuations of the...

We reinvestigate the 2D problem of the inhomogeneous incipient infinite cluster where, in an independent percolation model, the density decays to pc with an inverse power, [lambda], of the distance to the origin. Assuming the existence of critical exponents (as is known in the case of the...

The product of GIG and gamma distributions is preserved under the transformation (x,y)|-((x+y)-1,x-1-(x+y)-1). It is also known that this independence property may be reformulated and extended to an analogous property on trees. The purpose of this article is to show the independence property on...

We present a new technique for proving the empirical process invariance principle for stationary processes (Xn)n=0. The main novelty of our approach lies in the fact that we only require the central limit theorem and a moment bound for a restricted class of functions (f(Xn))n=0, not containing...

The first jump approximation of a pure jump Lévy process, which converges to the Lévy process in the Skorokhod topology in probability, is generalised to a multivariate setting and an infinite time horizon. It is shown that it can generally be used to obtain "first jump approximations" of...

We give a lower bound for the non-collision probability up to a long time T in a system of n independent random walks with fixed obstacles on . By 'collision' we mean collision between the random walks as well as collision with the fixed obstacles. We give an analogous result for Brownian...

In this note we present some examples of diffusions in random environment whose asymptotic behavior is rather surprising. We construct a family of diffusions that are small perturbations of Brownian motion with non-vanishing expected local drift under the static measure of the environment but...

Let [alpha][set membership, variant](0,2) and consider the operator for , where the [backward difference]f(x)[dot operator]h term is omitted if [alpha]1. We consider the martingale problem corresponding to the operator and under mild conditions on the function A prove that there exists a unique...