Intertwinings for general $β$ Laguerre and Jacobi processes

Theodoros Assiotis

Published 2016-09-13Version 1

We show that for $\beta \ge 1$ the semigroups of $\beta$ Laguerre and $\beta$ Jacobi processes of different dimensions are intertwined in analogy to a similar result for $\beta$ Dyson Brownian motion recently obtained by Ramanan and Shkolnikov. These intertwining relations generalize to arbitrary $\beta \ge 1$ the ones obtained for $\beta=2$ by the author, O'Connell and Warren between $h$-transformed Karlin-McGregor semigroups. Moreover they form the key first step towards constructing a multilevel process in a Gelfand Tsetlin pattern. Finally as a by product we obtain a relation between general $\beta$ Jacobi ensembles of different dimensions.