Random lazy random walks on arbitrary finite groups

This paper considers "lazy" random walks supported on a random subset of k elements of a finite group G with order n. If k [alog(2)n] where a >1 is co nstant, then most such walks take no more than a multiple of log(2) n steps to get close to uniformly distributed on G. If k=log(2)n+f(n) where f(n)-- > infinity and f(n)/log(2)n -->0 as n --> infinity, then most such walks ta ke no more than a multiple of (log(2)n) ln(log(2)n) steps to get close to u niformly distributed. To get these results, this paper extends techniques o f Erdos and Renyi and of Pak.