Random Walks on Randomly Evolving Graphs

Leran Cai, Thomas Sauerwald, Luca Zanetti

Abstract: A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution in time that is at most polynomial in the size of the graph. This fundamental property, however, only holds if the graph does not change over time; on the other hand, many distributed networks are inherently dynamic, and their topology is subjected to potentially drastic changes.