2020/02/03 by Andrii Ilienko, Ilienko, Andrii
Mathematics · #60C05 #60F05 #60G55 #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2002.00650
openalex publication_date 2020/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider an extended variant of the classical coupon collector's problem with infinite number of collections. An arriving coupon is placed in the rth collection, r≥0, if r is the smallest index such that the corresponding collection still does not have a coupon of this type. We derive distributional limit theorems for the number of empty spots in different collections at the time when the 0th collection was completed, as well as after some delay. We also obtain limiting distributions for completion times of different collections. All main results are given in an ultimate infinite-dimensional form in the sense of distributional convergence in \mathbb R^∞. The main tool in the proofs is convergence of specially constructed point processes.