KPZ equation limit of higher-spin exclusion processes

Ivan Corwin; Li Cheng Tsai

doi:10.1214/16-AOP1101

KPZ equation limit of higher-spin exclusion processes

Ivan Corwin
, Li Cheng Tsai

Research output: Contribution to journal › Article › peer-review

44 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1771-1798
Number of pages	28
Journal	Annals of Probability
Volume	45
Issue number	3
DOIs	https://doi.org/10.1214/16-AOP1101
State	Published - May 1 2017
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Exclusion processes
Higher-spin
Hopf-Cole transform
Kardar-Parisi- Zhang equation
Stochastic heat equation

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10.1214/16-AOP1101

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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.",

keywords = "Exclusion processes, Higher-spin, Hopf-Cole transform, Kardar-Parisi- Zhang equation, Stochastic heat equation",

author = "Ivan Corwin and Tsai, \{Li Cheng\}",

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AU - Corwin, Ivan

AU - Tsai, Li Cheng

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2017.

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Y1 - 2017/5/1

N2 - 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.

AB - 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.

KW - Exclusion processes

KW - Higher-spin

KW - Hopf-Cole transform

KW - Kardar-Parisi- Zhang equation

KW - Stochastic heat equation

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UR - https://www.scopus.com/pages/publications/85019257985#tab=citedBy

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JF - Annals of Probability

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ER -

KPZ equation limit of higher-spin exclusion processes

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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