The intertwining property for Laguerre processes with a fixed parameter

2024/03/18 by Alexander I. Bufetov, Bufetov, Alexander I., Yosuke Kawamoto +1 · 2 citations
Economics, Econometrics and Finance · Engineering · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2403.11718

openalex publication_date 2024/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the intertwining of Laguerre processes of parameter α in different dimensions. We introduce a Feller kernel that depends on α and intertwines the α-Laguerre process in N+1 dimensions and that in N dimensions. When α is a non-negative integer, the new kernel is interpreted in terms of the conditional distribution of the squared singular values: if the singular values of a unitarily invariant random matrix of order (N+α+1) × (N+1) are fixed, then the those of its (N+α) × N truncation matrix are given by the new kernel.

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• Boundary Feller-Dynkin processes associated with Laguerre processes and Pickrell diffusions
• The intertwining property for β-Laguerre processes and integral operators for Jack polynomials

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