Abstract
An ‘interacting particle system’ can be informally described as a Markov process consisting of countably many pure-jump processes that interact by modifying each other’s transition rates. Each individual pure-jump process in such a system is located at a ‘site’ and has state space {0,1,2,...,n}. The state of the pure-jump process at a given site is the number of ‘particles’ at that site, with n being the maximum particle number.
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References
Durrett, Richard, Lecture Notes on Particle Systems and Percolation, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, California, 1988.
Griffeath, David, Additive and Cancellative Interacting Particle Systems, Springer-Verlag, Berlin, 1979.
Georgii, Hans-Otto, Gibbs Measures and Phase Transitions, Walter de Gruyter, Berlin, 1988.
Grimmett, Geoffrey, Percolation, Springer-Verlag, New York, 1989.
Kesten, Harry, Percolation Theory for Mathematicians, Birkhäuser, Boston, 1982.
Khinchin, A. L, Mathematical Foundations of Statistical Mechanics, Dover, New York, 1949.
Kindermann, Ross and Snell, J. Laurie, Markov Random Fields and their Applications, American Mathematical Society, Providence, Rhode Island, 1980.
Liggett, Thomas M., Interacting Particle Systems, Springer-Verlag, New York, 1985.
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© 1997 Springer Science+Business Media New York
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Fristedt, B., Gray, L. (1997). Interacting Particle Systems. In: A Modern Approach to Probability Theory. Probability and its Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-2837-5_32
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DOI: https://doi.org/10.1007/978-1-4899-2837-5_32
Publisher Name: Birkhäuser, Boston, MA
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