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SUMMARY:From disorder relevance to the 2d Stochastic Heat Equation. - Niko
 laos Zygouras (Warwick)
DTSTART:20160426T153000Z
DTEND:20160426T163000Z
UID:TALK65363@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:We consider statistical mechanics models defined on a lattice\
 , such as pinning models\, directed polymers\, random field Ising model\, 
 in which disorder acts as an external random field. Such models are called
  disorder relevant\, if arbitrar- ily weak disorder changes the qualitativ
 e properties of the model. Via a Lindeberg principle for multilinear polyn
 omials we show that disorder relevance manifests it- self through the exis
 tence of a disordered high-temperature limit for the partition function\, 
 which is given in terms of Wiener chaos and is model specific.\nWhen disor
 der becomes marginally relevant a fundamentally new structure emerges\, wh
 ich leads to a universal scaling limit for all different (currently of dir
 ected poly- mer type) models that fall in this class. A notable such repre
 sentative is the two dimensional SHE with multipicative space-time white n
 oise (which in the SPDE language is characterised as “critical”). In t
 his case certain analogies with Gaussian Multiplicative Chaos and log-corr
 elated Gaussian fields appear.\nBased on joint works with Francesco Carave
 nna and Rongfeng Sun.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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