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Random walks on stochastic hyperbolic half planar triangulations
Author(s) -
Angel Omer,
Nachmias Asaf,
Ray Gourab
Publication year - 2016
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20625
Subject(s) - random walk , planar , mathematics , struct , boundary (topology) , simple (philosophy) , point (geometry) , simple random sample , combinatorics , statistical physics , discrete mathematics , mathematical analysis , pure mathematics , geometry , computer science , physics , statistics , sociology , population , philosophy , computer graphics (images) , demography , epistemology , programming language
We study the simple random walk on stochastic hyperbolic half planar triangulations constructed in (Angel and 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 ( − c n 1 / 3 ) © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 213–234, 2016