The Compulsive Gambler process
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Description: |
Aldous, D (University of California, Berkeley)
Tuesday 17 March 2015, 10:00-11:00 |
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Created: | 2015-03-18 13:00 |
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Collection: | Random Geometry |
Publisher: | Isaac Newton Institute |
Copyright: | Aldous, D |
Language: | eng (English) |
Distribution: | World (downloadable) |
Explicit content: | No |
Aspect Ratio: | 16:9 |
Screencast: | No |
Bumper: | UCS Default |
Trailer: | UCS Default |
Abstract: | Co-authors: Dan Lanoue (U.C. Berkeley), Justin Salez (Paris 7)
In the Compulsive Gambler process there are n agents who meet pairwise at random times (i and j meet at times of a rate-νij Poisson process) and, upon meeting, play an instantaneous fair game in which one wins the other's money. The process seems pedagogically interesting as being intermediate between coalescent-tree models and interacting particle models, and because of the variety of techniques available for its study. Some techniques are rather obvious (martingale structure; comparison with Kingman coalescent) while others are more subtle (an ``exchangeable over the money elements" property, and a ``token process" construction reminiscent of the Donnelly-Kurtz look-down construction). One can study both kinds of n→∞ 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 there is also a continuous-space extension called the Metric Coalescent. |
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