Pure and Applied Mathematics Quarterly

Volume 10 (2014)

Number 3

An explicit formula of hitting times for random walks on graphs

Pages: 567 – 581

DOI: http://dx.doi.org/10.4310/PAMQ.2014.v10.n3.a6


Hao Xu (Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang, China; and Department of Mathematics, University of Pittsburgh, Pennsylvania, U.S.A.)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)


We prove an explicit formula of hitting times in terms of enumerations of spanning trees for random walks on general connected graphs.We apply the formula to improve Lawler’s bound of hitting times for general graphs and derive closed formulas of hitting times for some special graphs.


random walk, hitting time, spanning tree

2010 Mathematics Subject Classification

Primary 05C81. Secondary 05C50, 60G50.

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