The Annals of Probability

KPZ equation limit of higher-spin exclusion processes

Ivan Corwin and Li-Cheng Tsai

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We prove that under a particular weak scaling, the 4-parameter interacting particle system introduced by Corwin and Petrov [Comm. Math. Phys. 343 (2016) 651–700] converges to the Kardar–Parisi–Zhang (KPZ) equation. This expands the relatively small number of systems for which weak universality of the KPZ equation has been demonstrated.

Article information

Ann. Probab., Volume 45, Number 3 (2017), 1771-1798.

Received: May 2015
Revised: December 2015
First available in Project Euclid: 15 May 2017

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C22: Interacting particle systems [See also 60K35] 82C23: Exactly solvable dynamic models [See also 37K60]

Exclusion processes Hopf–Cole transform higher-spin Kardar–Parisi–Zhang equation stochastic heat equation


Corwin, Ivan; Tsai, Li-Cheng. KPZ equation limit of higher-spin exclusion processes. Ann. Probab. 45 (2017), no. 3, 1771--1798. doi:10.1214/16-AOP1101.

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