Interlacing diffusions

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Title: Interlacing diffusions
Authors: O'Connell, Neil
Assiotis, Theodoros
Warren, Jon
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Date: 14-Feb-2019
Online since: 2019-05-07T11:41:33Z
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.
Funding Details: European Research Council
Type of material: Journal Article
Publisher: Cornell University
Keywords: ProbabilityMatrix valued diffusionsKarlin-McGregor semigroupsOne dimensional diffusion processesSiegmund duals
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Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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