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Square summability of variations of g-functions and uniqueness of g-measures
University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik. (Matematik)
2003 (English)In: Mathematical Research Letters, ISSN 1073-2780, Vol. 10, no 5, 587-601 p.Article in journal (Refereed) Published
Abstract [en]

We prove uniqueness of $g$-measures for $g$-functions satisfying quadratic summability of variations. Our result is in contrast to the situation of, \eg, the one-dimensional Ising model with long-range interactions, since $\ell_1$-summability of variations is required for general potentials. We illustrate this difference with some examples. To prove our main result we use a product martingale argument. We also give conditions for uniqueness of general $G$-measures, \ie, the case for general potentials, based on our investigation of the probabilistic case involving $g$-functions.

Place, publisher, year, edition, pages
2003. Vol. 10, no 5, 587-601 p.
Keyword [en]
Ergodic theory, Markov shifts, g-measures
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:hig:diva-2054ISI: 000188002600003OAI: oai:DiVA.org:hig-2054DiVA: diva2:118716
Available from: 2008-06-19 Created: 2008-06-19Bibliographically approved

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http://www.mrlonline.org/mrl/2003-010-005/2003-010-005-003.html

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