Recurrence of random walk traces

Abstract

We show that the edges crossed by a random walk in a network form a recurrent graph a.s. In fact, the same is true when those edges are weighted by the number of crossings.Comment: Published at http://dx.doi.org/10.1214/009117906000000935 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org