A Para-Controlled Approach to the Stochastic Yang-Mills Equation in Two Dimensions

Bjoern Bringmann; Sky Cao

doi:10.1090/memo/1624

A Para-Controlled Approach to the Stochastic Yang-Mills Equation in Two Dimensions

Bjoern Bringmann
, Sky Cao

Mathematics

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

Abstract

We consider the stochastic Yang-Mills heat equation on the two-dimensional torus. Using regularity structures, Chandra, Chevyrev, Hairer, and Shen previously proved both the local well-posedness and gauge-covariance of this model. In this article, we revisit their results using para-controlled calculus. One of the main ingredients is a new coordinate-invariant perspective on vector-valued stochastic objects.

Original language	English (US)
Journal	Memoirs of the American Mathematical Society
Volume	319
Issue number	1624
DOIs	https://doi.org/10.1090/memo/1624
State	Published - 2026

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

para-controlled calculus
singular SPDE
Yang-Mills

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10.1090/memo/1624

Cite this

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title = "A Para-Controlled Approach to the Stochastic Yang-Mills Equation in Two Dimensions",

abstract = "We consider the stochastic Yang-Mills heat equation on the two-dimensional torus. Using regularity structures, Chandra, Chevyrev, Hairer, and Shen previously proved both the local well-posedness and gauge-covariance of this model. In this article, we revisit their results using para-controlled calculus. One of the main ingredients is a new coordinate-invariant perspective on vector-valued stochastic objects.",

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AU - Bringmann, Bjoern

AU - Cao, Sky

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N2 - We consider the stochastic Yang-Mills heat equation on the two-dimensional torus. Using regularity structures, Chandra, Chevyrev, Hairer, and Shen previously proved both the local well-posedness and gauge-covariance of this model. In this article, we revisit their results using para-controlled calculus. One of the main ingredients is a new coordinate-invariant perspective on vector-valued stochastic objects.

AB - We consider the stochastic Yang-Mills heat equation on the two-dimensional torus. Using regularity structures, Chandra, Chevyrev, Hairer, and Shen previously proved both the local well-posedness and gauge-covariance of this model. In this article, we revisit their results using para-controlled calculus. One of the main ingredients is a new coordinate-invariant perspective on vector-valued stochastic objects.

KW - para-controlled calculus

KW - singular SPDE

KW - Yang-Mills

UR - https://www.scopus.com/pages/publications/105039101635

UR - https://www.scopus.com/pages/publications/105039101635#tab=citedBy

U2 - 10.1090/memo/1624

DO - 10.1090/memo/1624

M3 - Article

AN - SCOPUS:105039101635

SN - 0065-9266

VL - 319

JO - Memoirs of the American Mathematical Society

JF - Memoirs of the American Mathematical Society

IS - 1624

ER -

A Para-Controlled Approach to the Stochastic Yang-Mills Equation in Two Dimensions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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