Abstract
We consider consistent diffusion dynamics, leaving the celebrated HuaPickrell measures, depending on a complex parameter s, invariant. These, give rise to FellerMarkov processes on the infinite dimensional boundary Ω of the "graph of spectra", the continuum analogue of the GelfandTsetlin graph, via the method of intertwiners of Borodin and Olshanski. In the particular case of s=0, this stochastic process is closely related to the Sine2 point process on R that describes the spectrum in the bulk of large random matrices. Equivalently, these coherent dynamics are associated to interlacing diffusions in GelfandTsetlin patterns having certain Gibbs invariant measures. Moreover, under an application of the Cayley transform when s=0 we obtain processes on the circle leaving invariant the multilevel Circular Unitary Ensemble. We finally prove that the Feller processes on Ω corresponding to Dyson's Brownian motion and its stationary analogue are given by explicit and very simple deterministic dynamical systems.
Original language  English 

Pages (fromto)  12511283 
Journal  Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 
Volume  56 
Issue number  2 
Early online date  16 Mar 2020 
DOIs  
Publication status  Published  31 May 2020 
Fingerprint
Dive into the research topics of 'Hua–Pickrell diffusions and Feller processes on the boundary of the graph of spectra'. Together they form a unique fingerprint.Profiles

Theo Assiotis
 School of Mathematics  Lectureship/Readership in Probability and Stochastic Analysi
Person: Academic: Research Active (Teaching)