Random walks on Z2n

Paul Erdös and Robert W. Chen

Journal of Multivariate Analysis, 1988, vol. 25, issue 1, 111-118

Abstract: For each positive integer n >= 1, let Z2n be the direct product of n copies of Z2, i.e., Z2n = {(a1, a2, ..., an)[short parallel]ai = 0 or 1 for all I = 1, 2, ..., n} and let {Wtn}t>=0 be a random walk on Z2n such that P{W0n = A} = 2-n for all A's in Z2n and for all j = 0, 1, 2, ..., and all (a1, a2, ..., an)'s in Z2n. For each positive integer n >= 1, let Cn denote the covering time taken by the random walk Wtn on Z2n to cover Z2n, i.e., to visit every element of Z2n. In this paper, we prove that, among other results, P{except finitely many n, c2nln(2n)

Keywords: random; walks; Borel-Cantelli; lemma; covering; time (search for similar items in EconPapers)
Date: 1988
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