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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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.
|Journal or Publication Title:||Journal of the London Mathematical Society|
|Subjects:||Q Science > QA Mathematics|
|Departments:||Faculty of Science and Technology > Mathematics and Statistics|
|Deposited By:||Dr Alexander Belton|
|Deposited On:||26 Apr 2010 11:30|
|Last Modified:||26 Jul 2012 17:17|
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