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SUMMARY:The Anderson operator - Ismael Bailleul (Université de Rennes)
DTSTART:20220907T090000Z
DTEND:20220907T100000Z
UID:TALK178487@talks.cam.ac.uk
CONTACT:Jason Miller
DESCRIPTION:The continuous Anderson operator H is a perturbation of the La
 place-Beltrami operator by a random space white noise potential. We consid
 er this 'singular' operator on a two dimensional closed Riemannian manifol
 d. One can use functional analysis arguments to construct the operator as 
 an unbounded operator on L2 and give almost sure spectral gap estimates un
 der mild geometric assumptions on the Riemannian manifold. We prove a shar
 p Gaussian small time asymptotic for the heat kernel of H that leads among
 st others to strong norm estimates for quasimodes. We introduce a new rand
 om field\, called Anderson Gaussian free field\, and prove that the law of
  its random partition function characterizes the law of the spectrum of H.
  We also give a simple and short construction of the polymer measure on pa
 th space and prove large deviation results for the polymer measure and its
  bridges. We relate the Wick square of the Anderson Gaussian free field to
  the occupation measure of a Poisson process of loops of polymer paths.
LOCATION:MR9\, Centre for Mathematical Sciences
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