Random Walks and Percolation on Trees
Open Access
- 1 July 1990
- journal article
- research article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 18 (3) , 931-958
- https://doi.org/10.1214/aop/1176990730
Abstract
There is a way to define an average number of branches per vertex for an arbitrary infinite locally finite tree. It equals the exponential of the Hausdorff dimension of the boundary in an appropriate metric. Its importance for probabilistic processes on a tree is shown in several ways, including random walk and percolation, where it provides points of phase transition.Keywords
This publication has 1 reference indexed in Scilit:
- Bounds on the L 2 Spectrum for Markov Chains and Markov Processes: A Generalization of Cheeger's InequalityTransactions of the American Mathematical Society, 1988