On interweaving relations

Laurent Miclo, and Pierre Patie


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.


Interweaving relations; Laguerre processes; Hypoelliptic diffusions; Entropic convergence to equilibrium; Hyperboundedness;


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

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