Random walks on random simple graphs

This paper looks at random regular simple graphs and considers nearest neighbor random walks on such graphs. This paper considers walks where the degree d of each vertex is around (log n)(a), where a is a constant which is at least 2 and where n is the number of vertices. By extending techniques of Dou, this paper shows that for most such graphs, the position of the random walk becomes close to uniformly distributed after slightly more than log n/log d steps. This paper also gets similar results for the random graph G(n, p), where p = d/(n - 1). (C) 1996 John Wiley & Sons, Inc.