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math.PR2004★ 1 cited
Conceptual Proofs of L log L Criteria
Russell Lyons, Robin Pemantle, Yuval Peres
The Kesten-Stigum Theorem is a fundamental criterion for the rate of growth of a supercritical branching process, showing that an L log L condition is decisive. In critical and sub…
math.PR2004★ 2 cited
Random Walk in a Random Environment and First-Passage Percolation on Trees
Robin Pemantle, Russell Lyons
We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the…