Gambler's ruin in three dimensions.

Seminar: Probability Seminar | September 11 | 3:10-4 p.m. | 1011 Evans Hall

 Persi Diaconis, Stanford University

 Department of Statistics

Picture three gamblers with initial capital x(A), x(B), x(C) summing to N. Each time a pair of gamblers is chosen uniformly and they flip a fair coin. Consider the first time one of them hits zero.
How are the fortunes of the other two distributed and how does this depend on how they start?
Approximations (upper and lower bounds with reasonable constants) are derived for parallel problems on inner regular domains for countable state space Markov chains.
This is joint work with Kelsey Huston-Edwards and Laurent Saloff-Coste.