PC Seminar: The maximum number of coupons for the coupon collector

Abstract: In the classical coupon collector problem, there are n different types of coupons, and a person collects random coupons, where each coupon is uniformly distributed among the n types, and different coupons are independent. The person stops when he/she has at least one copuon of each type. The classical problem is about the total number of coupons collected, but also many other questions have been studied. I will talk about the largest number of coupons of any type, the second largest number and so on. This problem too has been studied before, but I think that a description involving a Poisson point process with all points rounded to integers is new.

This is a seminar in our seminar series on Probability and Combinatorics (PC).