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SUMMARY:Sourav Chatterjee (Stanford)
DTSTART:20211001T163000Z
DTEND:20211001T173000Z
DTSTAMP:20260423T005707Z
UID:PatC/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PatC/42/">Lo
 cal KPZ behavior under arbitrary scaling limits</a>\nby Sourav Chatterjee 
 (Stanford) as part of Probability and the City Seminar\n\n\nAbstract\nOne 
 of the main difficulties in proving convergence of discrete models of surf
 ace growth to the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher 
 than one is that the correct way to take a scaling limit\, so that the lim
 it is nontrivial\, is not known in a rigorous sense. The same problem has 
 so far prevented the construction of nontrivial solutions of the KPZ equat
 ion in dimensions higher than one. To understand KPZ growth without being 
 hindered by this issue\, I will introduce a new concept in this talk\, cal
 led "local KPZ behavior"\, which roughly means that the instantaneous grow
 th of the surface at a point decomposes into the sum of a Laplacian term\,
  a gradient squared term\, a noise term\, and a remainder term that is neg
 ligible compared to the other three terms and their sum. The main result i
 s that for a general class of surfaces\, which contains the model of direc
 ted polymers in a random environment as a special case\, local KPZ behavio
 r occurs under arbitrary scaling limits\, in any dimension.\n
LOCATION:https://researchseminars.org/talk/PatC/42/
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