"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
Keywords: Coalescing random walk, void zone, occupation time.
2000 Mathematics Subject Classification: 60G50; 60K35.