Random Walks in Dirichlet Environment (RWDE) correspond to Random Walks in Random
Environment (RWRE) on Zd where the transition probabilities are iid at each site with a …

Edge-reinforced random walk (ERRW), introduced by Coppersmith and Diaconis in 1986 [8],
is a random process which takes values in the vertex set of a graph G and is more likely to …

We study (unrooted) random forests on a graph where the probability of a forest is
multiplicatively weighted by a parameter β> 0 β> 0 per edge. This is called the arboreal gas …

We study how memory impacts passages at the origin for a so-called elephant random walk
in the diffusive regime. We observe that the number of zeros always grows asymptotically …

This paper concerns the vertex reinforced jump process (VRJP), the edge reinforced random
walk (ERRW), and their relation to a random Schrödinger operator. On infinite graphs, we …

We show transience of the edge-reinforced random walk (ERRW) for small reinforcement in
dimension d\ge3 d≥ 3. This proves the existence of a phase transition between recurrent …

We consider random walks on discrete state spaces, such as general undirected graphs,
where the random walkers are designed to approximate a target quantity over the network …

The classical random walk isomorphism theorems relate the local times of a continuous-time
random walk to the square of a Gaussian free field. A Gaussian free field is a spin system …

We prove the vertex-reinforced jump process (VRJP) is recurrent in two dimensions for any
translation invariant finite-range initial rates. Our proof has two main ingredients. The first is …

The vertex-reinforced jump process (VRJP), introduced by Davis and Volkov, is a continuous-
time process that tends to come back to already visited vertices. It is closely linked to the …