Random Walk on the Simple Symmetric Exclusion Process

Symmetric Simple Exclusion Process: Regularity of the Self Diffusion Coefficient

Symmetric Random Walk?)

Let Xk, k= 1, 2, 3, • • -, be a sequence of mutually independent random variables on an appropriate probability space which have a given common distribution function F. Let Sn = Xi+ • • • +Xn, then the event lim inf | S„\ = 0 has probability either zero or one. If this event has zero chance, we say F is transient; in the other case, | 5„| tends to infinity almost surely, and F is called recurre...

Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk

We prove an upper bound for the ǫ-mixing time of the symmetric exclusion process on any graph G, with any feasible number of particles. Our estimate is proportional to TRW(G) ln(|V |/ǫ), where |V | is the number of vertices in G and TRW(G) is the 1/4-mixing time of the corresponding single-particle random walk. This bound implies new results for symmetric exclusion on expanders, percolation clu...

The simple random walk on a random Voronoi tiling

Let P be a Poisson point process in Rd with intensity 1. We show that the simple random walk on the cells of the Voronoi diagram of P is almost surely recurrent in dimensions d = 1 and d = 2 and is almost surely transient in dimension d ≥ 3.

Large Favourite Sites of Simple Random Walk and the Wiener Process Large Favourite Sites of Simple Random Walk and the Wiener Process

Let U (n) denote the most visited point by a simple symmetric random walk fS k g k0 in the rst n steps. It is known that U (n) and max 0kn S k satisfy the same law of the iterated logarithm, but have diierent upper functions (in the sense of P. L evy). The distance between them however turns out to be transient. In this paper, we establish the exact rate of escape of this distance. The correspo...