Complex intertwinings and quantification of discrete free motions
ESAIM: Probability and Statistics, Tome 23 (2019), pp. 409-429.

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: ℤ$$, 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.

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DOI : 10.1051/ps/2018020
Classification : 81Q35, 47D08, 35K08, 39A12, 60J27
Mots-clés : Quantification, free motion, Markov process, Doob transform, intertwining
Miclo, Laurent 1

1 
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Miclo, Laurent. Complex intertwinings and quantification of discrete free motions. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 409-429. doi : 10.1051/ps/2018020. http://archive.numdam.org/articles/10.1051/ps/2018020/

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