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May 2021 Rates of convergence to equilibrium for potlatch and smoothing processes
Sayan Banerjee, Krzysztof Burdzy
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Ann. Probab. 49(3): 1129-1163 (May 2021). DOI: 10.1214/20-AOP1473

Abstract

We analyze the local and global smoothing rates of the smoothing process and obtain convergence rates to stationarity for the dual process known as the potlatch process. For general finite graphs we connect the smoothing and convergence rates to the spectral gap of the associated Markov chain. We perform a more detailed analysis of these processes on the torus. Polynomial corrections to the smoothing rates are obtained. They show that local smoothing happens faster than global smoothing. These polynomial rates translate to rates of convergence to stationarity in L2-Wasserstein distance for the potlatch process on Zd.

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Sayan Banerjee. Krzysztof Burdzy. "Rates of convergence to equilibrium for potlatch and smoothing processes." Ann. Probab. 49 (3) 1129 - 1163, May 2021. https://doi.org/10.1214/20-AOP1473

Information

Received: 1 March 2020; Revised: 1 May 2020; Published: May 2021
First available in Project Euclid: 7 April 2021

Digital Object Identifier: 10.1214/20-AOP1473

Subjects:
Primary: 60K35, 82C22
Secondary: 37A25, 60F25

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 3 • May 2021
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