"Large void zones and occupation times for coalescing random walks"

Endre Csáki, Pál Révész and Zhan Shi

The basic coalescing random walk is a system of interacting particles. These particles start from every site of d-dimensional integer lattice, and each moves independently as a continuous-time random walk. When two particles visit the same site, they coalesce into a single particle. We are interested in: (a) the radius of the largest ball centered at the origin which does not contain any particle at time T; and (b) the amount of time when the origin is occupied during [0,T]. We describe the almost sure asymptotic behaviours of these quantities.

Keywords: Coalescing random walk, void zone, occupation time.

2000 Mathematics Subject Classification: 60G50; 60K35.