Random walks on stochastic hyperbolic half planar triangulations. (English) Zbl 1344.05127
Summary: We study the simple random walk on stochastic hyperbolic half planar triangulations constructed in [the author and G. Ray, Ann. Probab. (in press)]. 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 \(\exp(-cn^{1/3})\).
MSC:
| 05C81 | Random walks on graphs |
| 05C80 | Random graphs (graph-theoretic aspects) |
| 05C10 | Planar graphs; geometric and topological aspects of graph theory |
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