A para-controlled approach to the stochastic Yang-Mills equation in two dimensions
Probability
2025-08-15 v2 Mathematical Physics
Analysis of PDEs
math.MP
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.
Keywords
Cite
@article{arxiv.2305.07197,
title = {A para-controlled approach to the stochastic Yang-Mills equation in two dimensions},
author = {Bjoern Bringmann and Sky Cao},
journal= {arXiv preprint arXiv:2305.07197},
year = {2025}
}
Comments
89 pages. Minor revisions. To appear in Mem. Amer. Math. Soc