No cut-off phenomenon for the “Insect Markov chain”

摘要

In this work we show that the probability measure associated with the Insect Markov chain defined on the ultrametric space of the leaves of the q-ary rooted tree of depth n ≥ 2 converges to the stationary distribution without a cut-off behavior. Keywords Rooted q-ary tree - Ultrametric space - Gelfand pairs - Spherical functions - Spectral analysis - k-Steps transition probability - Cut-off phenomenon Mathematics Subject Classification (2000) 60J10 - 43A85 - 43A90 - 05C05 - 05C25 Communicated by D. Elworthy.