Random walk on graphs with regular resistance and volume growth

2006/08/24 by András Telcs, Telcs, Andras
Mathematics · #35B05 #60J10 #60J45 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.math/0608594

openalex publication_date 2006/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper characterizations of graphs satisfying heat kernel estimates for a wide class of space-time scaling functions are given. The equivalence of the two-sided heat kernel estimate and the parabolic Harnack inequality is also shown via the equivalence of the upper (lower) heat kernel estimate to the parabolic mean value (and super mean value) inequality.

Citations

• On the parabolic kernel of the Schrödinger operator
• A new proof of Moser's parabolic harnack inequality using the old ideas of Nash

Related

• Random walks among time increasing conductances: heat kernel estimates
• Heat kernel estimates for strongly recurrent random walk on random media
• A note on heat kernel estimates, resistance bounds and Poincaré inequality
• Heat kernel estimates and related inequalities on metric graphs
• Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps