We consider the averaging process on a graph, that is the evolution of a mass distribu-tion undergoing repeated averages along the edges of the graph at the arrival times of independent Poisson processes. We establish cutoff phenomena for both the L1 and L2 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.
Cutoff for the averaging process on the hypercube and complete bipartite graphs / P. Caputo, M. Quattropani, F. Sau. - In: ELECTRONIC JOURNAL OF PROBABILITY. - ISSN 1083-6489. - 28:(2023), pp. EJP993.1-EJP993.32. [10.1214/23-EJP993]
Cutoff for the averaging process on the hypercube and complete bipartite graphs
F. SauUltimo
2023
Abstract
We consider the averaging process on a graph, that is the evolution of a mass distribu-tion undergoing repeated averages along the edges of the graph at the arrival times of independent Poisson processes. We establish cutoff phenomena for both the L1 and L2 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.
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