Interlacing Diffusions

Theodoros Assiotis, Neil O'Connell, JON WARREN

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We study in some generality intertwinings between h-transforms of Karlin–McGregor semigroups associated with one dimensional diffusion processes and those of their Siegmund duals. We obtain couplings so that the corresponding processes are interlaced and furthermore give formulae in terms of block determinants for the transition densities of these coupled processes. This allows us to build diffusion processes in the space of Gelfand–Tsetlin patterns so that the evolution of each level is Markovian. We show how known examples naturally fit into this framework and construct new processes related to minors of matrix valued diffusions. We also provide explicit formulae for the transition densities of the particle systems with one-sided collisions at either edge of such patterns.
Original languageEnglish
Title of host publicationSéminaire de Probabilités L
PublisherSpringer, Cham
Pages301-380
Number of pages80
ISBN (Electronic)978-3-030-28535-7
ISBN (Print)978-3-030-28534-0
DOIs
Publication statusPublished - 20 Nov 2019

Publication series

NameLecture Notes in Mathematics
PublisherSpringer, Cham
Volume2252

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