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SUMMARY:Quantitative sub-ballisticity of self-avoiding walk on the hexagon
 al lattice - Christoforos Panagiotis (University of Bath)
DTSTART:20240305T140000Z
DTEND:20240305T150000Z
UID:TALK212254@talks.cam.ac.uk
CONTACT:118195
DESCRIPTION:In this talk\, we will consider the self-avoiding walk on the 
 hexagonal lattice\, which is one of the few lattices whose connective cons
 tant can be computed explicitly. This was proved by Duminil-Copin and Smir
 nov in 2012 when they introduced the parafermionic observable. In this tal
 k\, we will use the observable to show that\, with high probability\, a se
 lf-avoiding walk of length n does not exit a ball of radius n/logn. This i
 mproves on an earlier result of Duminil-Copin and Hammond\, who obtained a
  non-quantitative o(n) bound. Along the way\, we show that at criticality\
 , the partition function of bridges of height T decays polynomially fast t
 o 0. Joint work with Dmitrii Krachun.
LOCATION:MR12
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