Volume 23, 2019
|Page(s)||409 - 429|
|Published online||12 July 2019|
Complex intertwinings and quantification of discrete free motions
Institut de Mathématiques de Toulouse, UMR 5219 Université de Toulouse and CNRS,
* Corresponding author: firstname.lastname@example.org
Accepted: 9 October 2018
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(ξL), when L is a (finite) Markov generator and ξ is a complex number of modulus 1.
Mathematics Subject Classification: 81Q35 / 47D08 / 35K08 / 39A12 / 60J27
Key words: Quantification / free motion / Markov process / Doob transform / intertwining
© The authors. Published by EDP Sciences, SMAI 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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