2014/09/05 by Brian Rider, Rider, Brian, Benedek Valkó +1
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1409.1954
openalex publication_date 2014/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a version of the classical Dufresne identity for matrix processes. In particular, we show that the inverse Wishart laws on the space of positive definite r x r matrices can be realized by the infinite time horizon integral of Mt times its transpose in which t -> Mt is a drifted Brownian motion on the general linear group. This solves a problem in the study of spiked random matrix ensembles which served as the original motivation for this result. Various known extensions of the Dufresne identity (and their applications) are also shown to have analogs in this setting. For example, we identify matrix valued diffusions built from Mt which generalize in a natural way the scalar processes figuring into the geometric Levy and Pitman theorems of Matsumoto and Yor.