Article

On interweaving relations

Laurent Miclo, and Pierre Patie

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;

Reference

Laurent Miclo, and Pierre Patie, On interweaving relations, Journal of Functional Analysis, vol. 280, n. 3, February 2021, 54 pages.

Published in

Journal of Functional Analysis, vol. 280, n. 3, February 2021, 54 pages