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SUMMARY:Directed polymers in random environment with heavy tails. - Oren L
 ouidor (NYU)
DTSTART:20091204T143000Z
DTEND:20091204T153000Z
UID:TALK21769@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 1/\\beta\, 
 we show strong localization of the polymer to an optimal region in the env
 ironment where energy and entropy are best balanced. We prove that this re
 gion has a weak limit under linear scaling and identify the limiting distr
 ibution as an (\\alpha\, \\beta)-indexed family of measures on Lipschitz c
 urves lying inside the 45'-rotated square with unit diagonal. In particula
 r\, this shows order of n for the transversal fluctuations of the polymer.
  If (and only if) \\alpha is small enough\, we find that there exists a ra
 ndom critical temperature above which the effect of the environment is not
  macroscopically noticeable. The results carry over to higher dimensions w
 ith minor modifications. Joint work with A. Auffinger .
LOCATION:Seminar Room 2\, Newton Institute Gatehouse.
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