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SUMMARY:Stochastic PDEs in terms of particle densities part.2
DTSTART:20120501T101500
DTEND:20120501T120000
DTSTAMP:20260916T050613Z
UID:a981dcf63000c55497280581358b60e598237f0704349c817e48cb4d
CATEGORIES:Conferences - Seminars
DESCRIPTION:Carl Mueller\nProbabilists have known for a long time that the
  solution of the heat equation can be viewed as the particle density of an
  infinite system of independent Brownian motions.  If the particles under
 go critical branching\, we obtain the well known super-Brownian motion.  
 This process is measure-valued\, and it satisfies a stochastic partial dif
 ferential equation (SPDE) in one dimension.  In higher dimensions\, it al
 so satisfies an SPDE\, but in the generalized sense.  This process was on
 e of the first examples of an SPDE related to a system of particles.\nIt t
 urns out to be possible to view many SPDE in terms of particle densities.
   This viewpoint is not only suggestive\, but has a rigorous formulation.
   In general\, the particles will no longer be independent.  But even so
 \, we often have enough information to prove interesting results.  Such r
 esults include blow-up\, traveling waves\, uniqueness and nonuniqueness\, 
 and even recent work on the KPZ equation.\nIn this mini-course\, I will gi
 ve the background for this approach and prove some of the most significant
  results.
LOCATION:AAC006 http://plan.epfl.ch/?zoom=20&recenter_y=5864224.42038&rece
 nter_x=730672.24955&layerNodes=fonds\,batiments\,labels\,information\,park
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STATUS:CONFIRMED
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