Cutoff for the Averaging process on the hypercube and complete bipartite graphs

Abstract

We consider the averaging process on a graph, that is the evolution of a mass distribution undergoing repeated averages along the edges of the graph at the arrival times of independent Poisson processes. We establish cutoff phenomena for both the $L^1$ and $L^2$ distance from stationarity when the graph is a discrete hypercube and when the graph is complete bipartite. Some general facts about the averaging process on arbitrary graphs are also discussed.

30 pages. Comments are welcome

References in corpus (3)

• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Separation cut-offs for birth and death chains
• On the mixing time and spectral gap for birth and death chains

Cited by in corpus (3)

• Concentration and local smoothness of the averaging process
• Tiny fluctuations of the averaging process around its degenerate steady state
• Finite-time consensus in a compromise process