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SUMMARY:Recent progress in multi-type WR models - Yuri Suhov (Cambridge &a
 mp\; Sao Paulo) 
DTSTART:20131203T140000Z
DTEND:20131203T150000Z
UID:TALK48910@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:The q-type WR (Widom--Rowlinson) model describes q species\nof
  particles/cells in d dimensions\, repelling each other when they\nbelong 
 to different species (a hard-core repulsion) and tolerating\neach other wh
 en they belong to the same species. For d at least 2 and\nq=2 (the origina
 l form of the model)\, if the densities of each type\nare high (and equal)
 \, the model is an example of non-uniqueness of \nshift-invariant ergodic 
 Gibbs/DLR measures (Ruelle\, 1972). Namely\,\nthere exist two such measure
 s\, they are generated by corresponding\nboundary conditions and are trans
 formed into each other\nby interchanging the types of particles.\n\nFor la
 rger values of q\, the picture is more complicated and depends on the\ncol
 lection of hard-core repulsion diameters. In the talk\, I'll give a\ncompl
 ete solution for q=3\,4 and discuss conjectures for q at least 5.\nIf the 
 time permits\, I'll touch on quantum aspects of the problem.\n\nThis is a 
 joint work with A. Mazel and I. Stuhl. No special preliminary\nknowledge i
 s expected from the audience\, either in Probability Theory or\nin Statist
 ical Mechanics.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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