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: | Article |
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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: | 07 Dec 2016 01:40 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/32894 |

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