Random walks on stochastic hyperbolic half planar triangulations. Issue 2 (20th June 2016)

• Record Type: Journal Article
• Authors: Angel, Omer; Nachmias, Asaf; Ray, Gourab
• Is Part Of: Random structures & algorithms. Volume 49:Issue 2(2016)
• Page Start: 213
• Page End: 234
• Publication Date: 2016-06-20
• Subjects: random graphs -- planar maps -- anchored expansion -- positive speed -- hyperbolic graph; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20625
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract: 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