Stationary distribution and cover time of random walks on random digraphs
We study properties of a simple random walk on the random digraph Dn,p when np = d log n , d>1.
We prove that whp the value πv of the stationary distribution at vertex v is asymptotic to deg−(v)/m where deg−(v) is the in-degree of v and m=n(n−1)p is the expected number of edges of Dn,p. If d=d(n)→∞ with n, the stationary distribution is asymptotically uniform whp.
Using this result we prove that, for d>1, whp the cover time of Dn,p is asymptotic to d log(d/(d − 1))n log n . If d=d(n)→∞ with n , then the cover time is asymptotic to n log n