Random Walks On The Random Graphs With Power Law Distribution

Abstract

We study the mixing time of the random walk on the random graphs with the power law degree distribution. In particular, we consider the case when the exponent $\gamma > 3$, the graph regime in which the distribution of the vertex degrees has finite first and second moments. We consider two different cases: start from a uniform vertex, and start from a high degree vertex. In both scenarios, the cutoff phenomena occurs.