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CATEGORIES:Probability
SUMMARY:The Anderson operator - Ismael Bailleul (Universit
é de Rennes)
DTSTART;TZID=Europe/London:20220907T100000
DTEND;TZID=Europe/London:20220907T110000
UID:TALK178487AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/178487
DESCRIPTION:The continuous Anderson operator H is a perturbati
on of the Laplace-Beltrami operator by a random sp
ace white noise potential. We consider this 'singu
lar' operator on a two dimensional closed Riemanni
an manifold. One can use functional analysis argum
ents to construct the operator as an unbounded ope
rator on L2 and give almost sure spectral gap esti
mates under mild geometric assumptions on the Riem
annian manifold. We prove a sharp Gaussian small t
ime asymptotic for the heat kernel of H that leads
amongst others to strong norm estimates for quasi
modes. We introduce a new random field\, called An
derson Gaussian free field\, and prove that the la
w of its random partition function characterizes t
he law of the spectrum of H. We also give a simple
and short construction of the polymer measure on
path space and prove large deviation results for t
he 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 lo
ops of polymer paths.
LOCATION:MR9\, Centre for Mathematical Sciences
CONTACT:Jason Miller
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