We study the local times of fractional Brownian motions for all temporal dimensions, N, spatial dimensions d and Hurst parameters H for which local times exist. We establish a Holder continuity result that is a refinement of Xiao (Probab Th Rel Fields 109: ...
We examine the long-range exclusion process introduced by Spitzer and studied by Liggett and answer some of the open questions raised by Liggett. In particular, we show the existence of equilibria corresponding to bounded dual harmonic functions and that t ...
We consider a model recently proposed by Chatterjee and Durrett [1] as an "annealed approximation" of boolean networks, which are a class of cellular automata on a random graph, as defined by S. Kauffman [5]. The starting point is a random directed graph o ...
We study the interface of the symmetric multitype contact process on Z. In this process, each site of Z is either empty or occupied by an individual of one of two species. Each individual dies with rate 1 and attempts to give birth with rate 2R lambda; the ...
We consider the contact process on a random graph with a fixed degree distribution given by a power law. We follow the work of Chatterjee and Durrett [2], who showed that for arbitrarily small infection parameter lambda, the survival time of the process is ...
We consider a symmetric, finite-range contact process with two types of infection; both have the same (supercritical) infection rate and heal at rate 1, but sites infected by Infection I are immune to Infection 2. We take the initial configuration where si ...
