On interweaving relations

Laurent Miclo and Pierre Patie
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Laurent Miclo: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, IMT - Institut de Mathématiques de Toulouse UMR5219 - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - UT - Université de Toulouse - UT2J - Université Toulouse - Jean Jaurès - UT - Université de Toulouse - UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique
Pierre Patie: CU - Cornell University [Ithaca]

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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 φ-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.

Keywords: Interweaving relations; Laguerre processes; Hypoelliptic diffusions; Entropic convergence to equilibrium; Hyperboundedness (search for similar items in EconPapers)
Date: 2021-02
Note: View the original document on HAL open archive server: https://hal.science/hal-03159496v1
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Published in Journal of Functional Analysis, 2021, 280 (3), ⟨10.1016/j.jfa.2020.108816⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03159496

DOI: 10.1016/j.jfa.2020.108816

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