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SUMMARY:An invariance principle for the 2d weakly self-repelling Brownian 
 polymer - Giuseppe Cannizzaro (University of Warwick)
DTSTART:20240709T091500Z
DTEND:20240709T101500Z
UID:TALK215569@talks.cam.ac.uk
DESCRIPTION:We investigate the large-scale behaviour of the Self-Repelling
  Brownian Polymer (SRBP) &nbsp\;in the critical dimension d=2. The SRBP is
  a model of self-repelling motion\, which is formally given by the solutio
 n to a stochastic differential equation driven by a standard Brownian moti
 on and with a drift given by the negative gradient of its own local time. 
 As with its discrete counterpart\, the "true" self-avoiding walk (TSAW) of
  [D.J. Amit\, G. Parisi\, L. Peliti\, Asymptotic behaviour of the ``true''
  self-avoiding walk\, Phys. Rev. B\, 1983]\, it is conjectured to be logar
 ithmically superdiffusive\, i.e. to be such that its mean-square displacem
 ent grows as t(log t)^b for t large and some currently unknown b in (0\,1)
 .\nThe main result of the paper is an invariance principle for the SRBP un
 der the weak coupling scaling\, which corresponds to scaling the SRBP diff
 usively and simultaneously tuning down the strength of the self-interactio
 n in a scale-dependent way. The diffusivity for the limiting Brownian moti
 on is explicit and its expression provides compelling evidence that the b 
 above should be 1/2. Further\, we derive the scaling limit of the so-calle
 d environment seen by the particle process\, which formally solves a non-l
 inear singular stochastic PDE of transport-type\, and prove this is given 
 by the solution of a stochastic linear transport equation with enhanced di
 ffusivity.&nbsp\;\nThis is join work with Harry Giles (University of Warwi
 ck\, UK).
LOCATION:Seminar Room 1\, Newton Institute
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