Journal of Statistical Physics

, Volume 10, Issue 1, pp 11–33

Gibbs and Markov random systems with constraints

  • John Moussouris
Articles

DOI: 10.1007/BF01011714

Cite this article as:
Moussouris, J. J Stat Phys (1974) 10: 11. doi:10.1007/BF01011714

Abstract

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.

Key words

Random systemMarkov assumptionlocal Markov conditionsGibbs potentialGibbs-Markov equivalenceinversion formula for potentialsconstraintsbarriers and wellslimit representationshigher-order equationsstrongly Markovian systems

Copyright information

© Plenum Publishing Corporation 1974

Authors and Affiliations

  • John Moussouris
    • 1
  1. 1.The Mathematical Institute and Merton CollegeOxfordEngland
  2. 2.Project MACMassachusetts Institute of TechnologyCambridge