Gibbs and Markov random systems with constraints
- John Moussouris
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This paper concerns random systems made up out of a finite collection of elements. We are interested in how a fixed structure of interactions reflects on the assignment of probabilities to overall states. In particular, we consider two simple models of random systems: one generalizing the notion of “Gibbs ensemble” abstracted from statistical physics; the other, “Markov fields” derived from the idea of a Markov chain. We give background for these two types, review proofs that they are in fact identical for systems with nonzero probabilities, and explore the new behavior that arises with constraints. Finally, we discuss unsolved problems and make suggestions for further work.
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- Gibbs and Markov random systems with constraints
Journal of Statistical Physics
Volume 10, Issue 1 , pp 11-33
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
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- Random system
- Markov assumption
- local Markov conditions
- Gibbs potential
- Gibbs-Markov equivalence
- inversion formula for potentials
- barriers and wells
- limit representations
- higher-order equations
- strongly Markovian systems
- Industry Sectors
- John Moussouris (1)
- Author Affiliations
- 1. The Mathematical Institute and Merton College, Oxford, England