Annals of Probability

Quantum Operators in Classical Probability Theory: II. The Concept of Duality in Interacting Particle Systems

Aidan Sudbury and Peter Lloyd

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Abstract

Duality has proved to be a powerful tool in the theory of interacting particle systems. The approach in this paper is algebraic rather than via Harris diagrams. A form of duality is found which includes coalescing and annihilating duality as special cases. This enables new results for the branching annihilating random walk and the biased annihilating branching process to be derived.

Article information

Source
Ann. Probab., Volume 23, Number 4 (1995), 1816-1830.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176987804

Digital Object Identifier
doi:10.1214/aop/1176987804

Mathematical Reviews number (MathSciNet)
MR1379169

Zentralblatt MATH identifier
0853.60079

JSTOR
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Interacting particle systems duality

Citation

Sudbury, Aidan; Lloyd, Peter. Quantum Operators in Classical Probability Theory: II. The Concept of Duality in Interacting Particle Systems. Ann. Probab. 23 (1995), no. 4, 1816--1830. doi:10.1214/aop/1176987804. https://projecteuclid.org/euclid.aop/1176987804


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See also

  • Part I: Peter Lloyd, Aidan Sudbury, Peter Donnelly. Quantum operators in classical probability theory. I. "Quantum spin'' techniques and the exclusion model of diffusion. Stochastic Proccess. Appl., vol. 61, no. 2, 205--221.
  • Part IV: Aidan Sudbury, Peter Lloyd. Quantum operators in classical probability theory. IV. Quasi-duality and thinnings of interacting particle systems.