On interweaving relations

Laurent Miclo (1, 2) , Pierre Patie

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 TSE-R - Toulouse School of Economics

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 classication 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.

Mots clés: interweaving relations; Laguerre processes; hypoelliptic di usions; entropic convergence to equilibrium; hyperboundedness

Domaines: Probabilités [math.PR]

Laurent Miclo, Pierre Patie. On interweaving relations. 2019. ⟨hal-02322294⟩