Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.12523 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915796261797888 |
|---|---|
| author | Correa, Jose Kiwi, Marcos Livanos, Vasilis Solan, Eilon Solan, Ron |
| author_facet | Correa, Jose Kiwi, Marcos Livanos, Vasilis Solan, Eilon Solan, Ron |
| contents | Consider the following process whereby $n$ balls are distributed into $k$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12523 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | About a Ball Removal Process on Bins Correa, Jose Kiwi, Marcos Livanos, Vasilis Solan, Eilon Solan, Ron Probability Optimization and Control Consider the following process whereby $n$ balls are distributed into $k$ 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. |
| title | About a Ball Removal Process on Bins |
| topic | Probability Optimization and Control |
| url | https://arxiv.org/abs/2602.12523 |