5 papers
On the minimum of independent collecting processes via the Stirling numbers of the second kind
Aristides V. Doumas
We consider the combinatorial problem where players aim to a complete set of different types of items (species) which are uniformly distributed. Let the random variables $T…
The Coupon Collector's Brother
Vassilis G. Papanicolaou, Aristides V. Doumas
A popular variant of the collector's problem is the following: Assume there are different types of coupons with equal occurring probabilities. There is one main collector who c…
On an Old Question of Erdős and Rényi Arising in the Delay Analysis of Broadcast Channels
Vassilis G. Papanicolaou, Aristides V. Doumas
Consider a broadcast channel with users, where different users receive different messages, and suppose that each user has to receive packets. A quantity of interest here, i…
Uniform versus Zipf distribution in a mixing collection process
Aristides V. Doumas, Vassilis G. Papanicolaou
We consider the following variant of the classic collector's problem: The family of coupon probabilities is the mixing of two subfamilies one of which is the \textit{uniform} famil…
A Randomized Version of the Collatz Problem
Aristides V. Doumas, Vassilis G. Papanicolaou
We propose a stochastic version of the Collatz Problem.