Large void zones and occupation times for coalescing random walks

Endre Csáki, Pál Révész and Zhan Shi

Stochastic Processes and their Applications, 2004, vol. 111, issue 1, 97-118

Abstract: The basic coalescing random walk is a system of interacting particles. These particles start from every site of , 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 Rd(T) of the largest ball centered at the origin which does not contain any particle at time T and (b) the amount of time [Lambda]d(T) when the origin is occupied during [0,T]. We describe the almost sure asymptotic behaviours of Rd(T) and [Lambda]d(T) (when T-->[infinity]), in three different regimes depending on whether d=1, d=2 or d[greater-or-equal, slanted]3.

Keywords: Coalescing; random; walk; Void; zone; Occupation; time (search for similar items in EconPapers)
Date: 2004
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