Quantum random walk approximation in Banach algebra

Belton's discrete approximation scheme is extended to Banach-algebra-valued sesquilinear quantum stochastic cocycles, through the dyadic discretisation of time. Approximation results for Markov-regular quantum stochastic mapping cocycles are recovered. We also obtain a new random walk approxima...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2015-10, Vol.430 (1), p.465-482
Main Authors: Das, B. Krishna, Lindsay, J. Martin
Format: Article
Language:English
Subjects:
Matrix space
Noncommutative probability
Quantum random walk
Quantum stochastic cocycle
Quantum Wiener integral
Sesquilinear process
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Summary:Belton's discrete approximation scheme is extended to Banach-algebra-valued sesquilinear quantum stochastic cocycles, through the dyadic discretisation of time. Approximation results for Markov-regular quantum stochastic mapping cocycles are recovered. We also obtain a new random walk approximation for a class of (not necessarily Markov-regular) isometric operator cocycles. Every Lévy process on a compact quantum group is implemented by a unitary cocycle from this class.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2015.02.039