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Volume and time doubling of graphs and random walks: The strongly recurrent case
Author(s) -
Telcs András
Publication year - 2001
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.1015
Subject(s) - mathematics , diagonal , harnack's inequality , random walk , harnack's principle , gaussian , volume (thermodynamics) , combinatorics , statistical physics , mathematical analysis , geometry , statistics , physics , quantum mechanics
This paper proves upper and lower off‐diagonal, sub‐Gaussian transition probability estimates for strongly recurrent random walks under sufficient and necessary conditions. Besides the known conditions, volume doubling and the elliptic Harnack inequality, a new property is introduced: time doubling. © 2001 John Wiley & Sons, Inc.