Random Walk in a Random Environment and First-passage Percolation on Trees
نویسندگان
چکیده
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 tree, which is a measure of the average number of branches per vertex. This generalizes and unifies previous work of the authors. It also shows that the point of phase transition for edge-reinforced random walk is likewise determined by the branching number of the tree. Finally, we show that the branching number determines the rate of first-passage percolation on trees, also known as the first-birth problem. Our techniques depend on quasi-Bernoulli percolation and large deviation results. §
منابع مشابه
Correction Random Walk in a Random Environment and First-passage Percolation on Trees by Russell Lyons
The proofs of Proposition 2 and of the first two parts of Theorem 3(ii) are incorrect, although the results themselves are correct. Here are correct proofs.
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