# Convergence of point processes associated with coupon collector's and Dixie cup problems

## TL;DR

This paper demonstrates that, in the coupon collector's problem, the normalized arrival times form a non-homogeneous Poisson process, enabling new generalizations of classical limit theorems in the field.

## Contribution

It establishes the convergence of point processes related to coupon collection times to a non-homogeneous Poisson process, extending classical results.

## Key findings

- Point processes converge to a non-homogeneous Poisson process
- Generalizations of classical limit theorems derived
- Infinite-dimensional extensions developed

## Abstract

We prove that, in the coupon collector's problem, the point processes given by the times of $r$-th arrivals for coupons of each type, centered and normalized in a proper way, converge toward a non-homogeneous Poisson point process. This result is then used to derive some generalizations and infinite-dimensional extensions of classical limit theorems on the topic.