Special Session 19: Stochastic Partial Differential Equations

Invariant measure of the 2D Yang-Mills Langevin dynamic

Hao Shen
University of Wisconsin - Madison
In an earlier work by Chandra, Chevyrev, Hairer and the speaker [CCHS] in 2020, we constructed an orbit space of the 2D Yang-Mills as well as a Markov process on the orbit space. In this talk, we prove that there exists a unique probability measure on the orbit space such that its finite dimensional distributions, seen as a process indexed by loops, agree with those of the YM measure in the sense of Levy`s earlier work in 2016. Moreover, this is the unique invariant probability measure on the orbit space for the Markov process in [CCHS]. Based on joint work with Ilya Chevyrev.