ASEP(q, j) converges to the KPZ equation

被引：31

作者：

Corwin, Ivan ^{[1
]}

Shen, Hao ^{[1
]}

Tsai, Li-Cheng ^{[1
]}

机构：

[1] Columbia Univ, Dept Math, 2990 Broadway, New York, NY 10027 USA

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2018年 / 54卷 / 02期

关键词：

ASEP(q; j); Gartner transformation; KPZ equation; STOCHASTIC BURGERS-EQUATION; EXCLUSION PROCESSES; PARTICLE-SYSTEMS; LIMIT;

D O I：

10.1214/17-AIHP829

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We show that a generalized Asymmetric Exclusion Process called 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.

引用

页码：995 / 1012

页数：18

共 28 条

[1] THE INTERMEDIATE DISORDER REGIME FOR DIRECTED POLYMERS IN DIMENSION 1+1 [J].

Alberts, Tom ;

Khanin, Konstantin ;

Quastel, Jeremy .

ANNALS OF PROBABILITY, 2014, 42 (03) :1212-1256

[2] Intermediate Disorder Regime for Directed Polymers in Dimension 1+1 [J].

Alberts, Tom ;

Khanin, Kostya ;

Quastel, Jeremy .

PHYSICAL REVIEW LETTERS, 2010, 105 (09)

[3] Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 Dimensions [J].

Amir, Gideon ;

Corwin, Ivan ;

Quastel, Jeremy .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2011, 64 (04) :466-537

[4] Stochastic burgers and KPZ equations from particle systems [J].

Bertini, L ;

Giacomin, G .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 183 (03) :571-607

[5]

Carinci G, 2016, PROBAB THEORY REL, V166, P887, DOI 10.1007/s00440-015-0674-0

[6]

Carinci G, 2016, J STAT PHYS, V163, P239, DOI 10.1007/s10955-016-1473-4

[7] KPZ EQUATION LIMIT OF HIGHER-SPIN EXCLUSION PROCESSES [J].

Corwin, Ivan ;

Tsai, Li-Cheng .

ANNALS OF PROBABILITY, 2017, 45 (03) :1771-1798

[8] Stochastic Higher Spin Vertex Models on the Line [J].

Corwin, Ivan ;

Petrov, Leonid .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2016, 343 (02) :651-700

[9] Weakly Asymmetric Non-Simple Exclusion Process and the Kardar-Parisi-Zhang Equation [J].

Dembo, Amir ;

Tsai, Li-Cheng .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2016, 341 (01) :219-261

[10] The Kardar-Parisi-Zhang Equation as Scaling Limit of Weakly Asymmetric Interacting Brownian Motions [J].

Diehl, Joscha ;

Gubinelli, Massimiliano ;

Perkowski, Nicolas .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2017, 354 (02) :549-589

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