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SUMMARY:Yang-Mills measure on the two-dimensional torus as a random distri
 bution - Ilya Chevyrev (University of Oxford)
DTSTART:20181123T110000Z
DTEND:20181123T123000Z
UID:TALK115096@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The Yang-Mills measure on a two-dimensional compact manifold h
 as been completely constructed as a stochastic process indexed by loops. I
 n this talk\, I will present a construction of the Yang-Mills measure on t
 he two-dimensional torus as a random distribution. More specifically\, I w
 ill introduce a space of distributional one-forms for which holonomies (i.
 e. Wilson loop observables) along axis paths are well-defined\, and show t
 hat there exists a random variable in this space which induces the Yang-Mi
 lls holonomies. An important feature of this space of one-forms is its emb
 edding into H&ouml\;lder-Besov spaces\, which commonly appear in the analy
 sis of stochastic PDEs\, with the small scale regularity expected from per
 turbation theory. The construction is based on a Landau-type gauge applied
  to lattice approximations.
LOCATION:Seminar Room 2\, Newton Institute
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