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SUMMARY:Paul Dario (Tel Aviv University)
DTSTART:20200525T120000Z
DTEND:20200525T130000Z
DTSTAMP:20260423T005840Z
UID:HSPETDS/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HSPETDS/7/">
 Large-scale behavior of the Villain model at low temperature in d = 3</a>\
 nby Paul Dario (Tel Aviv University) as part of Horowitz seminar on probab
 ility\, ergodic theory and dynamical systems\n\n\nAbstract\nIn this talk\,
  we will study the Villain rotator model in dimension three and prove that
 \, at low temperature\, the truncated two-point function of the model deca
 ys asymptotically like $|x|^{2-d}$\, with an algebraic rate of convergence
 . The argument starts from the observation that the asymptotic properties 
 of the Villain model are related to the large-scale behavior of a vector-v
 alued random surface with uniformly elliptic and infinite range potential\
 , following the arguments of Fröhlich\, Spencer and Bauerschmidt. We will
  then see that this behavior can be studied quantitatively by combining tw
 o sets of tools: the Helffer-Sjöstrand PDE\, initially introduced by Nadd
 af and Spencer to identify the scaling limit of the discrete Ginzburg-Land
 au model\, and the techniques of the quantitative theory of stochastic hom
 ogenization developed by Armstrong\, Kuusi and Mourrat. Joint work with We
 i Wu.\n
LOCATION:https://researchseminars.org/talk/HSPETDS/7/
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