Asymmetric Simple Exclusion Process with Open Boundaries and Quadratic Harnesses

We show that the joint probability generating function of the stationary measure of a finite state asymmetric exclusion process with open boundaries can be expressed in terms of joint moments of Markov processes called quadratic harnesses. We use our representation to prove the large deviations prin...

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Bibliographic Details
Published in:Journal of statistical physics 2017-04, Vol.167 (2), p.383-415
Main Authors: Bryc, Włodek, Wesołowski, Jacek
Format: Article
Language:English
Subjects:
Analysis
Boundaries
Harnesses
Infinity
Markov analysis
Markov processes
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Representations
Statistical Physics and Dynamical Systems
Theoretical
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Summary:We show that the joint probability generating function of the stationary measure of a finite state asymmetric exclusion process with open boundaries can be expressed in terms of joint moments of Markov processes called quadratic harnesses. We use our representation to prove the large deviations principle for the total number of particles in the system. We use the generator of the Markov process to show how explicit formulas for the average occupancy of a site arise for special choices of parameters. We also give similar representations for limits of stationary measures as the number of sites tends to infinity.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-017-1747-5