Random-walk approximation to vacuum cocycles
- Autores: Alexander C.R. Belton
- Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 81, Nº 2, 2010, págs. 412-434
- Idioma: inglés
- DOI: 10.1112/jlms/jdp075
- Enlaces
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Resumen
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�It�o 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.
