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SUMMARY:Directed polymers in random environment with heavy tails - Oren Lo
 uidor (NYU)
DTSTART:20091204T143000Z
DTEND:20091204T153000Z
UID:TALK21792@talks.cam.ac.uk
CONTACT:Berestycki
DESCRIPTION:We study the model of Directed Polymers in Random Environment 
 in 1+1 dimensions\, where the environment is i.i.d. with a site distributi
 on having a tail that decays regularly polynomially with power -\\alpha\, 
 where \\alpha \\in (0\,2). After proper scaling of temperature \\beta^{-1}
 \, we show strong localization of the polymer to an optimal region in the 
 environment where energy and entropy are best balanced. We prove that this
  region has a weak limit under linear scaling and identify the limiting di
 stribution as an (\\alpha\, \\beta)-indexed family of measures on Lipschit
 z curves lying inside the 45^{\\circ}-rotated square with unit diagonal. I
 n particular\, this shows order of n for the transversal fluctuations of t
 he polymer. If (and only if) \\alpha is small enough\, we find that there 
 exists a random critical temperature above which the effect of the environ
 ment is not macroscopically noticeable. The results carry over to higher d
 imensions with minor modifications. Joint work with A. Auffinger .
LOCATION:Newton Institute Gatehouse
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