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SUMMARY:Nicolas Perkowski (Freie Universität Berlin)
DTSTART:20201030T163000Z
DTEND:20201030T173000Z
DTSTAMP:20260423T024556Z
UID:PatC/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PatC/12/">Ma
 ss asymptotics for the 2d parabolic Anderson model with space white noise 
 potential</a>\nby Nicolas Perkowski (Freie Universität Berlin) as part of
  Probability and the City Seminar\n\n\nAbstract\nWe study the long time be
 havior of the total mass of the 2d parabolic Anderson model (PAM) with whi
 te noise potential\, which is the universal scaling limit of 2d branching 
 random walks in small random environments. There are several known results
  on the long time behavior of the PAM for more regular potentials\, but th
 e 2d white noise is very singular and it requires renormalization techniqu
 es. In particular\, the Feynman-Kac representation\, usually the main tool
  for deriving asymptotics\, breaks down. To overcome this problem we use a
  measure transform and we introduce a new "partial Feynman-Kac representat
 ion“. The new representation is based on a diffusion with distributional
  drift\, and we derive Gaussian heat kernel bounds for such diffusions. Ba
 sed on joint works with Wolfgang König and Willem van Zuijlen.\n
LOCATION:https://researchseminars.org/talk/PatC/12/
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