SOME RECENT PROGRESS IN SINGULAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

被引：21

作者：

Corwin, Ivan ^{[1
]}

Shen, Hao ^{[2
]}

机构：

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

[2] Univ Wisconsin, Dept Math, 480 Lincoln Dr, Madison, WI 53706 USA

来源：

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 2020年 / 57卷 / 03期

关键词：

PARABOLIC ANDERSON MODEL; BURGERS-EQUATION; KPZ EQUATION; WEAK UNIVERSALITY; HEAT-EQUATIONS; SCALING LIMIT; WHITE-NOISE; FLUCTUATIONS; ASEP; RENORMALIZATION;

D O I：

10.1090/bull/1670

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Stochastic partial differential equations are ubiquitous in mathematical modeling. Yet, many such equations are too singular to admit classical treatment. In this article we review some recent progress in defining, approximating, and studying the properties of a few examples of such equations. We focus mainly on the dynamical Phi(4) equation, the KPZ equation, and the parabolic Anderson model, as well as a few other equations which arise mainly in physics.

引用

页码：409 / 454

页数：46

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