Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.09114 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917363786448896 |
|---|---|
| author | Cohen, Serge Norris, James Pain, Michel Samorodnitsky, Gennady |
| author_facet | Cohen, Serge Norris, James Pain, Michel Samorodnitsky, Gennady |
| contents | We study sequences of partitions of the unit interval into subintervals, starting from the trivial partition, in which each partition is obtained from the one before by splitting its subintervals in two, according to a given rule, and then merging pairs of subintervals at the break points of the old partition. The $n$th partition then comprises $n+1$ subintervals with $n$ break points, which inherently possess an interlacing property. The empirical distribution of these points reveals a surprisingly rich structure, even when the splitting rule is completely deterministic. We consider both deterministic and randomized splitting rules and we study from multiple angles the limiting behavior of the empirical distribution of the break points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09114 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interlacing sequences resulting from an interval split-merge dynamics and the induced probability measures Cohen, Serge Norris, James Pain, Michel Samorodnitsky, Gennady Probability 60J05, 60F05 We study sequences of partitions of the unit interval into subintervals, starting from the trivial partition, in which each partition is obtained from the one before by splitting its subintervals in two, according to a given rule, and then merging pairs of subintervals at the break points of the old partition. The $n$th partition then comprises $n+1$ subintervals with $n$ break points, which inherently possess an interlacing property. The empirical distribution of these points reveals a surprisingly rich structure, even when the splitting rule is completely deterministic. We consider both deterministic and randomized splitting rules and we study from multiple angles the limiting behavior of the empirical distribution of the break points. |
| title | Interlacing sequences resulting from an interval split-merge dynamics and the induced probability measures |
| topic | Probability 60J05, 60F05 |
| url | https://arxiv.org/abs/2502.09114 |