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 and 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.
Funding Statement
P.C. thanks the Miller Institute for Basic Research in Science for funding his visit to UC Berkeley during the Fall 2022. M.Q. thanks the German Research Foundation (project number 444084038, priority program SPP2265) for financial support. F.S. gratefully acknowledges funding by the Lise Meitner fellowship, Austrian Science Fund (FWF): M3211. During the final stage of this work, F.S. was financially supported by “Microgrants 2022”, funded by Regione FVG, legge LR 2/2011.
Acknowledgments
F.S. wishes to thank Università Roma Tre, Dipartimento di Matematica e Fisica, for the very kind hospitality during an early stage of this work.
Citation
Pietro Caputo. Matteo Quattropani. Federico Sau. "Cutoff for the averaging process on the hypercube and complete bipartite graphs." Electron. J. Probab. 28 1 - 31, 2023. https://doi.org/10.1214/23-EJP993
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