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CATEGORIES:Probability
SUMMARY:Abelian sandpiles on infinite graphs - Antal Jarai
(Bath)
DTSTART;TZID=Europe/London:20110125T163000
DTEND;TZID=Europe/London:20110125T173000
UID:TALK28858AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/28858
DESCRIPTION:The Abelian sandpile model was introduced in the p
hysics literature as a toy model of "self-organize
d criticality". Originally\, it is defined as a Ma
rkov chain taking place on particle configurations
on a finite graph. It received a lot of attention
\, since several of its characteristics\, for exam
ple spatial correlations\, were observed to follow
power laws\, akin to critical systems in statisti
cal physics. In this talk\, I will give an overvie
w of results about limits on certain infinite grap
hs\, including the d-dimensional integer lattice.
I will also consider a perturbation of the model t
hat has exponential decay of correlations\, with r
ate of convergence estimates as the perturbation p
arameter vanishes. (In large part this is based on
joint works with S.R. Athreya\, R. Lyons\, F. Red
ig and E. Saada.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Berestycki
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