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SUMMARY:Stochastic heat equation and directed polymers in dimension d=2 - 
 Quentin Berger (Paris 13)
DTSTART:20251202T140000Z
DTEND:20251202T150000Z
UID:TALK237634@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:In this talk\, I will review some of the recent results on the
  Stochastic Heat Equation (SHE) with multiplicative white noise in dimensi
 on d=2. The SHE is a stochastic PDE which is ill-defined in its critical d
 imension d=2 : in that case\, very recent results show that a subtle norma
 lisation procedure is needed to make sense of it.\nI will present the prob
 abilistic approach to this normalisation procedure\, followed by Caravenna
 \, Sun\, Zygouras : it is based on the study of the directed polymer model
 \, a statistical mechanics model which can be seen as a discretised versio
 n of the SHE. In a very specific critical window for the parameters\, the 
 model possess a non-trivial scaling limit\, that Caravenna\, Sun\, Zygoura
 s called Critical 2D Stochastic Heat Flow\, and can be interpreted as a (n
 otion of a) solution to the 2D SHE.\nI will then review some of the proper
 ties of this Stochastic Heat Flow and present some of the results based on
  a joint work with F. Caravenna and N. Turchi.
LOCATION:MR12
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