About a Ball Removal Process on Bins
Probability
2026-02-16 v1 Optimization and Control
Abstract
Consider the following process whereby balls are distributed into bins. Repeatedly, a ball is removed from a non-empty bin chosen uniformly at random. The process ends when a single non-empty bin remains. Will Ma (see~\cite[Sec.~1.1]{GS24}) asked whether the initial assignment that minimizes the expected number of remaining balls is one that is as balanced as possible. Using a coupling argument we answer this conjecture positively, and we discuss the case of non-uniform choice among the non-empty bins.
Keywords
Cite
@article{arxiv.2602.12523,
title = {About a Ball Removal Process on Bins},
author = {Jose Correa and Marcos Kiwi and Vasilis Livanos and Eilon Solan and Ron Solan},
journal= {arXiv preprint arXiv:2602.12523},
year = {2026}
}