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arXiv · 1408.4196

Random walks on stochastic hyperbolic half planar triangulations

Omer Angel·Asaf Nachmias·Gourab Ray
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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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Omer Angel, Asaf Nachmias, Gourab Ray. 2014-08-19. Random walks on stochastic hyperbolic half planar triangulations. https://arxiv.org/abs/1408.4196

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