Interlacing sequences resulting from an interval split-merge dynamics and the induced probability measures
Abstract
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 nth 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.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Advanced Mathematical Identities
Random Matrices and Applications
Publication details
- Journal / source
- Latin American Journal of Probability and Mathematical Statistics
- Volume
- 23
- Issue
- 1
- Pages
- 583–583
- Publication date
- 1 January 2026
- Language
- EN