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.
Fields of Study & Subjects
Stochastic processes and financial applications
Geometric Analysis and Curvature Flows
advanced mathematical theories
Publication details
- Journal / source
- Memoirs of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Volume
- 319
- Issue
- 1624
- Publication date
- 28 April 2026
- Language
- EN