An invariance principle for branching diffusions in bounded domains

Distributed-order fractional diffusions on bounded domains

An averaging principle for fast diffusions in domains separated by semi-permeable membranes

We prove an averaging principle which asserts convergence of diffusions on domains separated by semi-permeable membranes, when the speed of diffusion tends to infinity while the flux through the membranes remains constant. In the limit, points in each domain are lumped into a single state of a limit Markov chain. The limit chain’s intensities are proportional to membranes’ permeability and inve...

An invariance principle for the edge of the branching exclusion process

We consider the one dimensional nearest neighbor branching exclusion process with initial configurations having a rightmost particle. We prove that, conveniently resealed, the position of the rightmost particle (edge) converges to a nondegenerate Brownian motion. Convergence to a convex combination of measures concentrating on the full and empty configurations at the average position of the edg...

An invariance principle for semimartingale reflecting Brownian motions in domains with piecewise smooth boundaries

Semimartingale reflecting Brownian motions (SRBMs) living in the closures of domains with piecewise smooth boundaries are of interest in applied probability because of their role as heavy traffic approximations for some stochastic networks. In this paper, assuming certain conditions on the domains and directions of reflection, a perturbation result, or invariance principle, for SRBMs is proved....

An invariance principle for random planar maps

We show a new invariance principle for the radius and other functionals of a class of conditioned ‘Boltzmann-Gibbs’distributed random planar maps. It improves over the more restrictive case of bipartite maps that was discussed in Marckert and Miermont (2006). As in the latter paper, we make use of a bijection between planar maps and a class of labelled multitype trees, due to Bouttier et al. (2...