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CATEGORIES:Probability
SUMMARY:Random lattice triangulations - Dr Alexandre Stauf
fer\, University of Bath
DTSTART;TZID=Europe/London:20140513T163000
DTEND;TZID=Europe/London:20140513T173000
UID:TALK52283AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/52283
DESCRIPTION:We consider lattice triangulations as triangulatio
ns of the integer points in the square [0\; n]x[0\
; n]. Our focus is on random triangulations in whi
ch the probability of obtaining a given lattice tr
iangulation T is proportional to \\lambda^|T|\, wh
ere \\lambda is a positive real parameter and |T|
is the total length of the edges in T. Empirically
\, this\nmodel exhibits a phase transition at \\la
mbda = 1 (corresponding to the uniform distributio
n): for \\lambda < 1 distant edges behave essentia
lly independently\, while for \\lambda > 1 very la
rge regions of aligned edges appear. We substantia
te\nthis picture as follows. For \\lambda < 1 suff
iciently small\, we show that correlations between
edges decay exponentially with distance (suitably
defined)\, and also that the Glauber dynamics (a
local Markov chain based on flipping edges) is ra
pidly mixing (in time polynomial in the number of
edges in the triangulation). By contrast\, for \\l
ambda > 1 we show that the mixing time is exponent
ial.\nJoint work with Pietro Caputo\, Fabio Martin
elli and Alistair Sinclair.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:
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