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Random walk on the incipient infinite cluster on trees. (English) Zbl 1110.60090

The authors study the continuous time simple random walk \(Y\) on the incipient infinite cluster \({\mathcal G}\) for percolation on a homogeneous tree of degree \(n_{0}+1\), and investigate quenched and annealed properties of its transition densities. One studies various quantities measuring behaviour of the process \(Y\): the transition density on the diagonal, the mean times to exit balls, the distance moved by the process from the starting point. For each of these quantities the authors discuss tightness, mean values and limiting behaviour. One also obtains annealed off-diagonal bounds for the density.

MSC:

60K37 Processes in random environments
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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