Article

Complex intertwinings and quantification of discrete free motions

Laurent Miclo

Abstract

The traditional quantification of free motions on Euclidean spaces into the Laplacian is revisited as a complex intertwining obtained through Doob transforms with respect to complex eigenvectors. This approach can be applied to free motions on finitely generated discrete Abelian groups: ℤm, with m ∈ ℕ, finite tori and their products. It leads to a proposition of Markov quantification. It is a first attempt to give a probability-oriented interpretation of exp(L), when L is a (finite) Markov generator and ξ is a complex number of modulus 1.

Reference

Laurent Miclo, Complex intertwinings and quantification of discrete free motions, ESAIM: Probability and Statistics , vol. 23, July 2019, pp. 409–429.

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Published in

ESAIM: Probability and Statistics, vol. 23, July 2019, pp. 409–429