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.
Citation
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
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