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SUMMARY:Scaling limits and decay of correlations for non-convex interactio
 n - Stefan Adams (Warwick)
DTSTART:20230613T130000Z
DTEND:20230613T140000Z
UID:TALK202480@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:We introduce a currently hot topic in probability theory\, the
  theory of scaling limits for random fields of gradients in all dimensions
 . The random fields are a class of model systems arising in the studies of
  random interfaces\, random geometry\, Euclidean field theory\, the theory
  of regularity structures\, and elasticity theory. After explaining how no
 n-convex energy terms can influence the scaling limit\, we outline our res
 ult on the scaling limit to the continuum Gaussian Free Field in dimension
  d=2\,3 for a class of non-convex interaction energies. We show that the H
 essian of the free energy governs the continuum Gaussian Free Field. The s
 econd result concern the Gaussian decay of correlations. All our results h
 old in the low-temperature regime and moderate boundary tilts. We outline 
 how multi-scale/renormalisation group methods provide means of proving our
  statements.
LOCATION:MR14
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