Green function estimates and their applications to the intersections of symmetric random walks

Xian Yin Zhou

Stochastic Processes and their Applications, 1993, vol. 48, issue 1, 31-60

Abstract: In this paper, a Harnack inequality for some difference operators arising from uniform symmetric random walks (see Definition 1.1 below) on is proved, and a criterion on the intersections of two independent random walks on graphs is derived. As applications, we obtain reasonable estimates for the Green functions of uniform symmetric random walks on . We also prove that the intersections of two independent uniform symmetric random walks on can occur infinitely often with probability one if d[greater-or-equal, slanted]4 and with probability zero if d[greater-or-equal, slanted]5, as for simple random walks on .

Keywords: Green; function; electrical; network; effective; resistance; Harnack; inequality; intersection; Wiener; test (search for similar items in EconPapers)
Date: 1993
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