Ergodicity of multiplicative statistics

2009/01/29 by Yu. V. Yakubovich, Yuri Yakubovich, Yakubovich, Yuri
Mathematics · #05A17 #60B10 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Statistical Methods and Models #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #math.CO #math.PR #msc:05A17 #msc:60B10

paper · pdf · doi:10.48550/arxiv.0901.4655

22 pages; added some references and corrected some typos

openalex publication_date 2009/01/29 · arxiv created 2009/04/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a subfamily of multiplicative measures on integer partitions we give conditions for properly rescaled associated Young diagrams to converge in probability to a certain deterministic curve named the limit shape of partitions. We provide explicit formulas for the scaling function and the limit shape covering some known and some new examples.

Related

• Limit shapes of multiplicative measures associated with coagulation-fragmentation processes and random combinatorial structures
• The limit shape of random permutations with polynomially growing cycle weights
• Equivalence of ensembles under inhomogeneous conditioning and its applications to random Young diagrams
• Asymptotic joint distribution of the extremities of a random Young diagram and enumeration of graphical partitions
• A note on monotone subsequences and the RS image of invariant random permutations with macroscopic number of fixed points