The Simple Random Walk Snake on Z^4 is Recurrent

Details The Simple Random Walk Snake on Z^4 is Recurrent The Simple Random Walk Snake on Z^4 is Recurrent

2011-07-06

arxiv.org/abs/1107.1226v1

Mathematics

Probability

Scientific paper

Consider the branching simple random walk on Z^d indexed by a critical
geometric Galton-Watson tree conditioned to survive. Using the concept of
unimodular random graphs, we show that the walk is recurrent if and only if d
is less than or equal to 4.

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