About this Event
View mapSpeaker: Hao Shen (University of Wisconsin, Madison)
Title: Invariant measure and universality of the 2D Yang-Mills Langevin dynamic
Abstract: In [CCHS20] by Chandra, Chevyrev, Hairer and S., a Langevin dynamic for 2D Yang-Mills (YM) was constructed on 2D torus. In this talk we discuss some new results based on a joint paper with Chevyrev [CS23]. We prove that the 2D YM measure is invariant for the Langevin dynamic constructed in [CCHS20]. Our argument relies on a combination of regularity structures, lattice gauge-fixing, and Bourgain’s method for invariant measures. In particular, we prove a universality result which states that for a wide class of lattice YM gauge theories, their corresponding Langevin dynamics converge to the same continuum dynamic constructed in [CCHS20]. An important step is a proof of uniqueness for the mass renormalisation of the gauge-covariant continuum Langevin dynamic, which allows us to identify the limit of discrete approximations. As corollaries we obtain a gauge-fixed decomposition of the YM measure into a Gaussian free field and an almost Lipschitz remainder, and a proof of universality for the 2D YM measure under a wide class of discrete approximations.