The differential equations associated with Calogero-Moser-Sutherland particle models in the freezing regime

2019/10/17 by Michael Voit, Voit, Michael, Jeannette H. C. Woerner +1 · 2 citations
Mathematics · #33C45 #34A05 #60B20 #60F05 #60J60 #82C22 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1910.07888

openalex publication_date 2019/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Multivariate Bessel processes describe Calogero-Moser-Sutherland particle models and are related with β-Hermite and β-Laguerre ensembles. They depend on a root system and a multiplicity k. Recently, several limit theorems for k→∞ were derived where the limits depend on the solutions of associated ODEs in these freezing regimes. In this paper we study the solutions of these ODEs which are are singular on the boundaries of their domains. In particular we prove that for a start in arbitrary boundary points, the ODEs always admit unique solutions in their domains for t>0.

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