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

Siva Athreya, Antar Bandyopadhyay, Amites Dasgupta and Neeraja Sahasrabudhe

Stochastic Processes and their Applications, 2022, vol. 146, issue C, 80-97

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.

Keywords: Random walk on free group; Random walk in random environment; Trees; Transience; Central limit theorem; Positive speed (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2021.12.009

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