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SUMMARY:Random lattice triangulations - Dr Alexandre Stauffer\, University
  of Bath 
DTSTART:20140513T153000Z
DTEND:20140513T163000Z
UID:TALK52283@talks.cam.ac.uk
CONTACT:37296
DESCRIPTION:We consider lattice triangulations as triangulations of the in
 teger points in the square [0\; n]x[0\; n]. Our focus is on random triangu
 lations in which the probability of obtaining a given lattice triangulatio
 n T is proportional to \\lambda^|T|\, where \\lambda is a positive real pa
 rameter and |T| is the total length of the edges in T. Empirically\, this\
 nmodel exhibits a phase transition at \\lambda = 1 (corresponding to the u
 niform distribution): for \\lambda < 1 distant edges behave essentially in
 dependently\, while for \\lambda > 1 very large regions of aligned edges a
 ppear. We substantiate\nthis picture as follows. For \\lambda < 1 sufficie
 ntly small\, we show that correlations between edges decay exponentially w
 ith distance (suitably defined)\, and also that the Glauber dynamics (a l
 ocal Markov chain based on flipping edges) is rapidly mixing (in time poly
 nomial in the number of edges in the triangulation). By contrast\, for \\l
 ambda > 1 we show that the mixing time is exponential.\nJoint work with Pi
 etro Caputo\, Fabio Martinelli and Alistair Sinclair.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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