  Random walks are used for modeling various dynamics in, for example,
physical, biological, and social contexts. Furthermore, their characteristics
provide us with useful information on the phase transition and critical
phenomena of even broader classes of related stochastic models. Abundant
results are obtained for random walk on simple graphs such as the regular
lattices and the Cayley trees. However, random walks and related processes on
more complex networks, which are often more relevant in the real world, are
still open issues, possibly yielding different characteristics. In this paper,
we investigate the return times of random walks on random graphs with arbitrary
vertex degree distributions. We analytically derive the distributions of the
return times. The results are applied to some types of networks and compared
with numerical data.
