Complex intertwinings and quantification of discrete free motions

Résumé

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.

Référence

Laurent Miclo, « Complex intertwinings and quantification of discrete free motions », ESAIM: Probability and Statistics , vol. 23, juillet 2019, p. 409–429.