Random-walk approximation to vacuum cocycles

Belton, Alexander C. R. (2010) Random-walk approximation to vacuum cocycles. Journal of the London Mathematical Society, 81 (2). pp. 412-434. ISSN 1469-7750

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Abstract

Quantum random walks are constructed on operator spaces with the aid of matrix-space lifting, a type of ampliation intermediate between those provided by spatial and ultraweak tensor products. Using a form of Wiener–Ito decomposition, a Donsker-type theorem is proved, showing that these walks, after suitable scaling, converge in a strong sense to vacuum cocycles: these are vacuum-adapted processes that are Feller cocycles in the sense of Lindsay and Wills. This is employed to give a new proof of the existence of ∗-homomorphic quantum-stochastic dilations for completely positive contraction semigroups on von Neumann algebras and separable unital C∗ algebras. The analogous approximation result is also established within the standard quantum stochastic framework, using the link between the two types of adaptedness.

Item Type:
Journal Article
Journal or Publication Title:
Journal of the London Mathematical Society
Uncontrolled Keywords:
/dk/atira/pure/researchoutput/libraryofcongress/qa
Subjects:
ID Code:
32894
Deposited By:
Deposited On:
26 Apr 2010 10:30
Refereed?:
Yes
Published?:
Published
Last Modified:
19 Feb 2020 07:59

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