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Yang-Mills measure on the two-dimensional torus as a random distribution

Presented by: 
Ilya Chevyrev University of Oxford
Date: 
Friday 23rd November 2018 - 11:00 to 12:30
Venue: 
INI Seminar Room 2
Abstract: 
The Yang-Mills measure on a two-dimensional compact manifold has been completely constructed as a stochastic process indexed by loops. In this talk, I will present a construction of the Yang-Mills measure on the two-dimensional torus as a random distribution. More specifically, I will introduce a space of distributional one-forms for which holonomies (i.e. Wilson loop observables) along axis paths are well-defined, and show that there exists a random variable in this space which induces the Yang-Mills holonomies. An important feature of this space of one-forms is its embedding into Hölder-Besov spaces, which commonly appear in the analysis of stochastic PDEs, with the small scale regularity expected from perturbation theory. The construction is based on a Landau-type gauge applied to lattice approximations.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons