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January 1997 Quantum operators in classical probability theory. IV. Quasi-duality and thinnings of interacting particle systems
Peter Lloyd, Aidan Sudbury
Ann. Probab. 25(1): 96-114 (January 1997). DOI: 10.1214/aop/1024404280

Abstract

Duality has proved to be a powerful technique in the study of interacting particle systems (IPS). This concept can be enlarged and a “quasi-duality” defined between various pairs of IPS previously thought unrelated. Consequently, theorems of a similar style to those involving duality can be deduced.

The concept of quasi-duality follows naturally from our previous studies into the use of “single-site operators” (an idea borrowed from quantum physics) in paper II of this series. It is shown that a necessary condition for quasi-duality is that the eigenvalues of the corresponding two-site infinitesimal generators be the same, and, using this observation, a number of quasi-dual pairs have been found and studied.

It is further shown that if two different IPS share a common dual, then one can be considered as a “thinning” of the other.

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Peter Lloyd. Aidan Sudbury. "Quantum operators in classical probability theory. IV. Quasi-duality and thinnings of interacting particle systems." Ann. Probab. 25 (1) 96 - 114, January 1997. https://doi.org/10.1214/aop/1024404280

Information

Published: January 1997
First available in Project Euclid: 18 June 2002

zbMATH: 0873.60075
MathSciNet: MR1428501
Digital Object Identifier: 10.1214/aop/1024404280

Subjects:
Primary: 60K35

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 1 • January 1997
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