VARIATIONAL PRINCIPLE FOR FUZZY GIBBS MEASURES

Evgeny Verbitskiy*

*Corresponding author for this work

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    Abstract

    In this paper we study a large class of renormalization transformations of measures on lattices. An image of a Gibbs measure under such transformation is called a fuzzy Gibbs measure. Transformations of this type and fuzzy Gibbs measures appear naturally in many fields. Examples include the hidden Markov processes (HMP), memory-less channels in information theory, continuous block factors of symbolic dynamical systems, and many renormalization transformations of statistical mechanics. The main result is the generalization of the classical variational principle of Dobrushin-Lanford-Ruelle for Gibbs measures to the class of fuzzy Gibbs measures.

    Original languageEnglish
    Pages (from-to)811-829
    Number of pages19
    JournalMoscow mathematical journal
    Volume10
    Issue number4
    Publication statusPublished - 2010

    Keywords

    • Non-Gibbsian measures
    • renormalization
    • deterministic and random transformations
    • variational principle
    • TO-ONE CODES
    • TRANSFORMATIONS
    • PROJECTIONS
    • ENTROPY
    • STATES
    • MODEL

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