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SUMMARY:The Compulsive Gambler process - Aldous\, D (University of Califor
 nia\, Berkeley)
DTSTART:20150317T100000Z
DTEND:20150317T110000Z
UID:TALK58427@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-authors: Dan Lanoue (U.C. Berkeley)\, Justin Salez (Paris 7
 ) \n\nIn the Compulsive Gambler process there are $n$ agents who meet pair
 wise at random times ($i$ and $j$ meet at times of a rate-$\nu_{ij}$ Poiss
 on process) and\, upon meeting\, \nplay an instantaneous fair game in whic
 h one wins the other's money.  \nThe process seems pedagogically interesti
 ng as being intermediate between coalescent-tree models and interacting pa
 rticle models\, and because of the variety of techniques available for its
  study. Some techniques are rather obvious (martingale structure\; compari
 son with Kingman coalescent) while others are more subtle (an ``exchangeab
 le \nover the money elements" property\, and a ``token process" constructi
 on reminiscent of the Donnelly-Kurtz look-down construction). One can stud
 y both kinds of $n 	o infty$ limit. The process can be defined under weak 
 assumptions on a countable discrete space (nearest-neighbor interaction on
  trees\, or long-range interaction on the $d$-dimensional lattice) and the
 re is also a continuous-space extension called the Metric Coalescent. \n
LOCATION:Seminar Room 1\, Newton Institute
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