Random walks on stochastic hyperbolic half planar triangulations

2014/08/19 by Omer Angel, Angel, Omer, Asaf Nachmias +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1408.4196

30 pages

arxiv created 2014/08/19 · arxiv updated 2014/08/20

Abstract

We study the simple random walk on stochastic hyperbolic half planar triangulations constructed in Angel and Ray [3]. We show that almost surely the walker escapes the boundary of the map in positive speed and that the return probability to the starting point after n steps scales like exp(-cn^1/3).

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