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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.

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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: Article
Journal or Publication Title: Journal of the London Mathematical Society
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 32894
Deposited By: Dr Alexander Belton
Deposited On: 26 Apr 2010 11:30
Refereed?: Yes
Published?: Published
Last Modified: 09 Apr 2014 21:48
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/32894

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