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SUMMARY:Bulk deviations for the simple random walk - Alberto Chiarini (Uni
 versità degli Studi di Padova)
DTSTART:20241031T114500Z
DTEND:20241031T124500Z
UID:TALK220738@talks.cam.ac.uk
DESCRIPTION:In this talk we aim at establishing large-deviation estimates 
 for the probability that the average value over a large box of some local 
 observable of the field of occupation times of the simple random walk exce
 eds a given positive value. When the rare event occurs\, we are in the pre
 sence of a certain &ldquo\;high density regime&rdquo\; and the random walk
  is locally well approximated by random interlacements with a slowly varyi
 ng intensity. This can be used as a pivotal tool to obtain exact exponenti
 al rates for the probability of the deviant behaviour. In fact\, the proof
  of the lower bound relies on the introduction of a near optimal strategy 
 via the so called tilted walks - originally constructed by Li (2017) - whi
 ch can be coupled with random interlacements at mesoscopic scales. Importa
 ntly\, the lower bound matches at leading order the corresponding upper bo
 und derived by Sznitman (2023)\, and is given in terms of a certain constr
 ained variational problem. As an application\, we look into the question o
 f how costly it is for the simple random walk to disconnect an excessive f
 raction of points from an enclosing box. The talk is based on the joint wo
 rk with M. Nitzschner (Hong Kong University of Science and Technology).
LOCATION:Seminar Room 1\, Newton Institute
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