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: email@example.com
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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.