Convergence of Coupon Collecting Process via Wormald's Differential Equation Method

TL;DR

This paper applies Wormald's differential equation method to analyze the convergence of coupon collecting processes, providing a new approach to understanding the classical problem in probability and combinatorics.

Contribution

It introduces a novel application of differential equation techniques to track all coupons in the collection process, extending previous methods.

Findings

Demonstrates convergence of coupon collecting process trajectories

Provides a detailed differential equation framework for analysis

Enhances understanding of coupon collector's problem dynamics

Abstract

To approximate the trajectories of a stochastic process by the solution of some differential equation is widely used in the fields of probability, computer science and combinatorics. In this paper, the convergence of coupon collecting processes is studied via the differential equation techniques originally proposed in Wormald(1995) and modified in Warnke(2019). In other words, we give a novel approach to analysis the classical coupon collector's problem and keep track of all coupons in the process of collecting.