skip to content
 

The Compulsive Gambler process

Date: 
Tuesday 17th March 2015 - 10:00 to 11:00
Venue: 
INI Seminar Room 1
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-$\nu_{ij}$ 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 $n \to \infty$ 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 there is also a continuous-space extension called the Metric Coalescent.

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons