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Large Deviation Behavior of Statistical Mechanics Models in the Multiphase Regime

In: Mathematical Physics X

Author

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  • R. L. Dobrushin

    (Institute for Problems of Information Transmission
    Massachusetts Institute of Technology)

  • S. B. Shlosman

    (Institute for Problems of Information Transmission)

Abstract

The theory of large deviations was initiated by the study of the asymptotical behavior of probabilities of large deviations of sums of n identically distributed independent random variables. In this case the logarithms of the probabilities are asymptotically equal to -nI, where I is a constant which can be defined by a minimization of the so-called action functional. The theory of large deviations is now a well-developed branch of the probability theory (see the books [1], [2] for example) devoted mainly to generalization of the mentioned asymptotics to wide classes of random processes. Also these types of results were recently generalized on a wide class of Gibbsian random fields (see [3], [4]).

Suggested Citation

  • R. L. Dobrushin & S. B. Shlosman, 1992. "Large Deviation Behavior of Statistical Mechanics Models in the Multiphase Regime," Springer Books, in: Konrad Schmüdgen (ed.), Mathematical Physics X, pages 328-332, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-77303-7_31
    DOI: 10.1007/978-3-642-77303-7_31
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