Time evolution of averaged limit shapes of random multiple Young diagrams

2025/09/09 by Akihito Hora, Hora, Akihito
Computer Science · Mathematics · #20C30 #20C35 #46L54 #60J28 #82C41 #FOS: Mathematics #Geometry and complex manifolds #Probability (math.PR) #Representation Theory (math.RT) #Stochastic processes and statistical mechanics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2509.07393

openalex publication_date 2025/09/09 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

The branching rule for the tower of wreath products of a finite group by the symmetric groups induces a stochastic process on the set of multiple Young diagrams through random transitions of boxes of the diagrams between one another. We observe dynamical multiple averaged limit shapes resulting from appropriate scaling limits, either diffusive or non-diffusive. We describe time evolution of the macroscopic multiple averaged limit shapes in terms of Voiculescu's R-transforms and free Lévy measures of corresponding Kerov transition measures. Our microscopic dynamics admits non-exponential pausing time distributions.

Citations

• Dynamical Spin Limit Shape of Young Diagram and Spin Jucys-Murphy Elements for Symmetric Groups
• Effect of microscopic pausing time distributions on the dynamical limit shapes for random Young diagrams
• Stein's Method, Jack Measure, and the Metropolis Algorithm
• Stein's Method and Plancherel Measure of the Symmetric Group
• Approximate factorization and concentration for characters of symmetric groups

Related

• Effect of microscopic pausing time distributions on the dynamical limit shapes for random Young diagrams
• The limit shape of random permutations with polynomially growing cycle weights
• Kerov's central limit theorem for the Plancherel measure on Young diagrams
• Edge fluctuations of limit shapes
• Random Young diagrams in a Rectangular Box