Complex intertwinings and quantification of discrete free motions
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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.
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2011 ◽
Vol 10
(03)
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pp. 377-389
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1969 ◽
Vol 21
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pp. 702-711
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1996 ◽
Vol 39
(3)
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pp. 294-307
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1969 ◽
Vol 21
◽
pp. 684-701
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1996 ◽
Vol 19
(3)
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pp. 539-544
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