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Mathematics > Probability

arXiv:2111.10652 (math)
[Submitted on 20 Nov 2021 (v1), last revised 25 Aug 2022 (this version, v4)]

Title:The Yang-Mills heat flow with random distributional initial data

Authors:Sky Cao, Sourav Chatterjee
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Abstract:We construct local solutions to the Yang-Mills heat flow (in the DeTurck gauge) for a certain class of random distributional initial data, which includes the 3D Gaussian free field. The main idea, which goes back to work of Bourgain as well as work of Da Prato-Debussche, is to decompose the solution into a rougher linear part and a smoother nonlinear part, and to control the latter by probabilistic arguments. In a companion work, we use the main results of this paper to propose a way towards the construction of 3D Yang-Mills measures.
Comments: 79 pages. Minor changes in this revision
Subjects: Probability (math.PR); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Analysis of PDEs (math.AP)
MSC classes: 35R60, 35A01, 60G60, 81T13
Cite as: arXiv:2111.10652 [math.PR]
  (or arXiv:2111.10652v4 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.2111.10652

Submission history

From: Sourav Chatterjee [view email]
[v1] Sat, 20 Nov 2021 18:37:23 UTC (73 KB)
[v2] Wed, 1 Dec 2021 07:09:16 UTC (73 KB)
[v3] Sat, 12 Mar 2022 16:32:11 UTC (73 KB)
[v4] Thu, 25 Aug 2022 18:25:49 UTC (83 KB)
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