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|Title:||Interlacing diffusions||Authors:||O'Connell, Neil
|Permanent link:||http://hdl.handle.net/10197/10314||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:||Probability; Matrix valued diffusions; Karlin-McGregor semigroups; One dimensional diffusion processes; Siegmund duals||Other versions:||https://arxiv.org/abs/1607.07182v3||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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