SLLN and annealed CLT for random walks in I.I.D. random environment on Cayley trees

Authors

Siva Athreya, Indian Statistical Institute Bangalore
Antar Bandyopadhyay, Indian Statistical Institute (Delhi Centre)
Amites Dasgupta, Indian Statistical Institute, Kolkata
Neeraja Sahasrabudhe, Indian Institute of Science Education and Research Mohali

Article Type

Research Article

Publication Title

Stochastic Processes and their Applications

Abstract

We consider the random walk in an independent and identically distributed (i.i.d.) random environment on a Cayley graph of a finite free product of copies of Z and Z2. Such a Cayley graph is readily seen to be a regular tree. Under a uniform ellipticity assumption on the i.i.d. environment we show that the walk has positive speed and establish the annealed central limit theorem for the graph distance of the walker from the starting point.

First Page

80

Last Page

97

DOI

10.1016/j.spa.2021.12.009

Publication Date

4-1-2022

Recommended Citation

Athreya, Siva; Bandyopadhyay, Antar; Dasgupta, Amites; and Sahasrabudhe, Neeraja, "SLLN and annealed CLT for random walks in I.I.D. random environment on Cayley trees" (2022). Journal Articles. 3188.
https://digitalcommons.isical.ac.in/journal-articles/3188