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Large void zones and occupation times for coalescing random walks

Author

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  • Csáki, Endre
  • Révész, Pál
  • Shi, Zhan

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.

Suggested Citation

  • Csáki, Endre & Révész, Pál & Shi, Zhan, 2004. "Large void zones and occupation times for coalescing random walks," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 97-118, May.
    • Handle: RePEc:eee:spapps:v:111:y:2004:i:1:p:97-118
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