On interweaving relations



Miclo, Laurent and Patie, Pierre ORCID: 0000-0003-4221-0439
(2021) On interweaving relations. Journal of Functional Analysis, 280 (3).

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Abstract

Interweaving relations are introduced and studied here in a general Markovian setting as a strengthening of usual intertwining relations between semigroups, obtained by adding a randomized delay feature. They provide a new classification scheme of the set of Markovian semigroups which enables to transfer from a reference semigroup and up to an independent warm-up time, some ergodic, analytical and mixing properties including the $\varphi$-entropy convergence to equilibrium, the hyperboundedness and when the warm-up time is deterministic the cut-off phenomena. We also present several useful transformations that preserve interweaving relations. We provide a variety of examples of interweaving relations ranging from classical, discrete, and non-local Laguerre and Jacobi semigroups to degenerate hypoelliptic Ornstein-Uhlenbeck semigroups and some non-colliding particle systems.

Item Type: Article
Uncontrolled Keywords: math.PR, math.PR, math.AP, interweaving relations, Laguerre processes, hypoelliptic diffusions, entropic convergence to equilibrium, hyperboundedness
Depositing User: Symplectic Admin
Date Deposited: 08 Jan 2021 14:26
Last Modified: 04 Mar 2021 00:11
DOI: 10.1016/j.jfa.2020.108816
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3112847