The Annals of Probability

Heat kernel upper bounds for interacting particle systems

Arianna Giunti, Yu Gu, and Jean-Christophe Mourrat

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Abstract

We show a diffusive upper bound on the transition probability of a tagged particle in the symmetric simple exclusion process. The proof relies on optimal spectral gap estimates for the dynamics in finite volume, which are of independent interest. We also show off-diagonal estimates of Carne–Varopoulos type.

Article information

Source
Ann. Probab., Volume 47, Number 2 (2019), 1056-1095.

Dates
Received: September 2016
Revised: April 2018
First available in Project Euclid: 26 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.aop/1551171645

Digital Object Identifier
doi:10.1214/18-AOP1279

Mathematical Reviews number (MathSciNet)
MR3916942

Zentralblatt MATH identifier
07053564

Subjects
Primary: 82C22: Interacting particle systems [See also 60K35] 35B65: Smoothness and regularity of solutions
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Heat kernel estimate interacting particle system exclusion process

Citation

Giunti, Arianna; Gu, Yu; Mourrat, Jean-Christophe. Heat kernel upper bounds for interacting particle systems. Ann. Probab. 47 (2019), no. 2, 1056--1095. doi:10.1214/18-AOP1279. https://projecteuclid.org/euclid.aop/1551171645


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