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SUMMARY:Spectral gap critical exponent for Glauber dynamics of hierarchica
 l spin models - Roland Bauerschmidt (University of Cambridge)
DTSTART:20180907T080000Z
DTEND:20180907T090000Z
UID:TALK109309@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We develop a renormalisation group approach to deriving the as
 ymptotics of the spectral gap of the generator of Glauber type dynamics of
  spin systems at and near a critical point. In our approach\, we derive a 
 spectral gap inequality\, or more generally a Brascamp--Lieb inequality\, 
 for the measure recursively in terms of spectral gap or Brascamp--Lieb ine
 qualities for a sequence of renormalised measures. We apply our method to 
 hierarchical versions of the $4$-dimensional $n$-component $|\\varphi|^4$ 
 model at the critical point and its approach from the high temperature sid
 e\, and the $2$-dimensional Sine--Gordon and the Discrete Gaussian models 
 in the rough phase (Kosterlitz--Thouless phase). For these models\, we sho
 w that the spectral gap decays polynomially like the spectral gap of the d
 ynamics of a free field (with a logarithmic correction for the $|\\varphi|
 ^4$ model)\, the scaling limit of these models in equilibrium.  Co-author:
  Thierry Bodineau
LOCATION:Seminar Room 1\, Newton Institute
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