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SUMMARY:A dynamical system of the WR model in 1D  - Dr Yuri Suhov\, Statsl
 ab/University of Sao Paulo\, Brazil 
DTSTART:20140415T131500Z
DTEND:20140415T141500Z
UID:TALK52022@talks.cam.ac.uk
CONTACT:37296
DESCRIPTION:A one-dimensional Widom--Rowlinson model with $q$ types of\npa
 rticles is considered from a dynamical\npoint of view.  Particles of a uni
 t mass move along the line without\nnoticing each other when they belong t
 o the same type and experiencing\nelastic collisions when they belong to d
 ifferent types. A natural\ninvariant\n(equilibrium) measure is where (i) t
 he position distribution\nrepresents a shift-invariant point process forme
 d\nby random (Poissonian/geometric) `series` of particles of  a fixed\ntyp
 e succeeded by series of other types separated\nfrom each other by hard-co
 re exclusion intervals\, and (ii) the\nvelocities of different particles\n
 are IID. We show that an `equilibrium` dynamical system with such an\ninva
 riant measure has extreme\nergodic properties (generates a B-flow of an in
 finite entropy).\nMoreover\, we check that a `non-equilibrium`\nflow\, wit
 h an initial distribution of a general type\, exhibits\nconvergence to a l
 imiting measure of the above form.\n\nAll concepts from the ergodic theory
  will be introduced on the spot\,\nincluding a brief history of the Botzma
 nn ergodicity conjecture\n(featured prominently in this year's Abel prtize
  citation.)
LOCATION:MR15\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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