The Annals of Probability

KPZ equation limit of higher-spin exclusion processes

Ivan Corwin and Li-Cheng Tsai

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aop/1494835231

Digital Object Identifier
doi:10.1214/16-AOP1101

Mathematical Reviews number (MathSciNet)
MR3650415

Zentralblatt MATH identifier
06754786

Subjects
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]

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

Citation

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. https://projecteuclid.org/euclid.aop/1494835231


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References

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