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Subdiffusive behavior of random walk on a random cluster. (English) Zbl 0632.60106
Consider a particle performing a symmetric random walk on a random graph G, when G is either the family tree of a critical branching process conditioned on non-extinction, or the incipient infinite cluster of bond percolation on the two-dimensional square lattice.
In both cases the author investigates the mean square displacement of the walker, showing that it is subdiffusive in the sense that it grows at most as $$n^{\alpha}$$ for $$\alpha <1$$. In the former case it is shown that, when normalized by $$n^{1/3}$$, the displacement of the walker has a limiting distribution.
Reviewer: G.R.Grimmet

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 60G50 Sums of independent random variables; random walks
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