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SUMMARY:On the Range of a Random Walk In a Torus - Eric Shellef (Weizmann 
 Institute)
DTSTART:20100615T153000Z
DTEND:20100615T163000Z
UID:TALK24882@talks.cam.ac.uk
CONTACT:Berestycki
DESCRIPTION:Let a simple random walk run inside a torus of dimension three
  or higher for a number of steps which is a constant proportion of the vol
 ume. We examine geometric properties of the range\, the random subgraph in
 duced by the set of vertices visited by the walk. Distance and mixing boun
 ds for the typical range are proven that are a k-iterated log factor from 
 those on the full torus for arbitrary k. The proof uses hierarchical renor
 malization and techniques that can possibly be applied to other random pro
 cesses in the Euclidean lattice.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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