Discrete Green's functions and random walks on graphs

Authors:
Hao Xu;Shing-Tung Yau
Affiliations:
Department of Mathematics, Harvard University, Cambridge, MA 02138, USA;Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
Venue:
Journal of Combinatorial Theory Series A
Year:
2013

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Abstract

We prove an explicit formula of Chung-Yau@?s Discrete Green@?s functions as well as hitting times of random walks on graphs. The formula is expressed in terms of two natural counting invariants of graphs. Uniform derivations of Green@?s functions and hitting times for trees and other special graphs are given.