  We consider a random model for directed graphs whereby an arc is placed from
one vertex to another with a prescribed probability which may vary from arc to
arc. Using perturbation bounds as well as Chernoff inequalities, we show that
the stationary distribution of a Markov process on a random graph is
concentrated near that of the "expected" process under mild conditions. These
conditions involve the ratio between the minimum and maximum in- and
out-degrees, the ratio of the minimum and maximum entry in the stationary
distribution, and the smallest singu- lar value of the transition matrix.
Lastly, we give examples of applications of our results to well-known models
such as PageRank and G(n, p).
