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SUMMARY:Continuous-time weakly self-avoiding walk on Z has strictly monoto
 ne escape speed - Yucheng Liu (University of British Columbia)
DTSTART:20240709T143000Z
DTEND:20240709T150000Z
UID:TALK215578@talks.cam.ac.uk
DESCRIPTION:Weakly self-avoiding walk is a model of simple random walk pat
 hs that penalizes self-intersections. On Z\, Greven and den Hollander prov
 ed in 1993 that the discrete-time weakly self-avoiding walk has an asympto
 tically deterministic escape speed\, and they conjectured that this speed 
 should be strictly increasing in the repelling strength parameter.&nbsp\;W
 e study a continuous-time version of the model\, give a different existenc
 e proof for the speed\, and prove the speed to be strictly increasing. The
  proof uses a transfer matrix method implemented via a supersymmetric vers
 ion of the BFS--Dynkin isomorphism theorem\, spectral theory\, Tauberian t
 heory\, and stochastic dominance.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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