Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

$\operatorname{ASEP}(q,j)$ converges to the KPZ equation

Ivan Corwin, Hao Shen, and Li-Cheng Tsai

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Abstract

We show that a generalized Asymmetric Exclusion Process called $\operatorname{ASEP}(q,j)$ introduced in (Probab. Theory Related Fields 166 (2016) 887–933). converges to the Cole–Hopf solution to the KPZ equation under weak asymmetry scaling.

Résumé

Nous montrons qu’une généralisation du processus d’exclusion asymétrique appelée $\operatorname{ASEP}(q,j)$, introduite dans (Probab. Theory Related Fields 166 (2016) 887–933), converge sous faible asymétrie vers la solution de l’équation KPZ au sens de Cole–Hopf.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 54, Number 2 (2018), 995-1012.

Dates
Received: 3 October 2016
Revised: 31 December 2016
Accepted: 17 March 2017
First available in Project Euclid: 25 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1524643237

Digital Object Identifier
doi:10.1214/17-AIHP829

Mathematical Reviews number (MathSciNet)
MR3795074

Zentralblatt MATH identifier
06897976

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 82C22: Interacting particle systems [See also 60K35]

Keywords
$\operatorname{ASEP}(q,j)$ Gärtner transformation KPZ equation

Citation

Corwin, Ivan; Shen, Hao; Tsai, Li-Cheng. $\operatorname{ASEP}(q,j)$ converges to the KPZ equation. Ann. Inst. H. Poincaré Probab. Statist. 54 (2018), no. 2, 995--1012. doi:10.1214/17-AIHP829. https://projecteuclid.org/euclid.aihp/1524643237


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