Tuesday, Feb. 10, 11:00-12:00

Random walks are widely examined, and their characteristics provide us with useful information 

on 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.  We investigate the return times of random walks on random graphs with arbitrary 

vertex degree distributions. We derive the distributions of the first and general return times.