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CATEGORIES:Probability
SUMMARY:Delocalization of uniform graph homomorphisms from
Z^2 to Z - Martin Tassy (Dartmouth)
DTSTART;TZID=Europe/London:20180807T140000
DTEND;TZID=Europe/London:20180807T150000
UID:TALK108847AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/108847
DESCRIPTION:Graph homomorphisms from the Zd lattice to Z are f
unctions on Zd whose gradients equal 1 in absolute
value. These functions are the height functions c
orresponding to proper 3-colorings of Zd and\, in
two dimensions\, corresponding to the 6-vertex mod
el (square ice). We show that the model delocalize
s in two dimensions\, having no translation-invari
ant Gibbs measures for the uniform sampling subjec
t to boundary conditions. We also obtain additiona
l results in higher dimensions including the fact
s that every ergodic Gibbs measure is extremal and
that the ergodic Gibbs measures are stochasticall
y ordered. The proof follows interesting but littl
e known arguments presented by Scott Sheffield in
Random surface which are adapted and simplified to
the present settings.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Perla Sousi
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