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SUMMARY:Abelian sandpiles on infinite graphs - Antal Jarai (Bath)
DTSTART:20110125T163000Z
DTEND:20110125T173000Z
UID:TALK28858@talks.cam.ac.uk
CONTACT:Berestycki
DESCRIPTION:The Abelian sandpile model was introduced in the physics liter
 ature as a toy model of "self-organized criticality". Originally\, it is d
 efined as a Markov chain taking place on particle configurations on a fini
 te graph. It received a lot of attention\, since several of its characteri
 stics\, for example spatial correlations\, were observed to follow power l
 aws\, akin to critical systems in statistical physics. In this talk\, I wi
 ll give an overview of results about limits on certain infinite graphs\, i
 ncluding the d-dimensional integer lattice. I will also consider a perturb
 ation of the model that has exponential decay of correlations\, with rate 
 of convergence estimates as the perturbation parameter vanishes. (In large
  part this is based on joint works with S.R. Athreya\, R. Lyons\, F. Redig
  and E. Saada. 
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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