Random walks on stochastic hyperbolic half planar triangulations
  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 $\exp(-cn^{1/3})$. 
Omer Angel, Asaf Nachmias and Gourab Ray
math.PR