Cut-off and Escape Behaviors for Birth and Death Chains on Trees
arXiv:1006.4324
Abstract
We consider families of discrete time birth and death chains on trees, and show that in presence of a drift towards the root of the tree, the chains exhibit cut-off behavior along the drift and escape behavior in the opposite direction.
22 pages, 1 figure. This new version, written after referee's suggestions, is shorter and features a more clear presentation of the results. The previous proofs of Section 3, based on difference equations method, are now given in appendix