Friday, 15 March, 2013
SPEAKER: Prof. Vasilis Papanicolaou - Washington Univ., St. Louis and
National Technical University of Athens, Greece
TITLE: Asymptotics and Limit Distributions for the General Collectors Problem
ABSTRACT: Let $T_N$ be the number of coupons that a collector has to buy in order to
find all $N$ existing different coupons. The probabilities (occurring frequencies) of the coupons
can be quite arbitrary. Using the asymptotics of the expectation and variance of $T_N$ as $N to
infty$ and the general limit theorems of P. Neal, we derive the limit distribution of $T_N$ (appropriately normalized), which, for a large class of probabilities, turns out to be the standard Gumbel distribution. Our results extend a well-known result of P. Erdos and A. Renyi.
Joint work with Aris tides V. Doumas.
Refreshments will be available at 3:10 p.m.