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SUMMARY:Condensation of a self-attracting random walk - Nathanael Berestyc
 ki (Cambridge)
DTSTART:20160119T150000Z
DTEND:20160119T160000Z
UID:TALK63938@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:I will introduce a Gibbs distribution on nearest-neighbour pat
 hs of length t in the Euclidean d-dimensional lattice\, where each path is
  penalised by a factor proportional to the size of its boundary and an inv
 erse temperature \\beta. This model can be thought of as a random walk ver
 sion of the Wulff crystal problem in percolation or the Ising model. \n\nI
 n joint work with Ariel Yadin we prove that\, for all \\beta>0\, the rando
 m walk condensates to a set of diameter (t/\\beta) ^  {1/3} in dimension d
 =2\, up to a multiplicative constant. In all dimensions d\\ge 3\, we also 
 prove that the volume is bounded above by (t/\\beta) ^  {d/(d+1)} and the 
 diameter is bounded below by (t/\\beta) ^  {1/(d+1)}.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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