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Shannon-McMillan theorems for discrete random fields along curves and lower bounds for surface-order large deviations
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Brettschneider, Julia (2008) Shannon-McMillan theorems for discrete random fields along curves and lower bounds for surface-order large deviations. Probability Theory and Related Fields, Volume 142 (Numbers 3-4). pp. 443-473. doi:10.1007/s00440-007-0112-z ISSN 0178-8051.
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Official URL: http://dx.doi.org/10.1007/s00440-007-0112-z
Abstract
The notion of a surface-order specific entropy h(c) (P) of a two-dimensional discrete random field P along a curve c is introduced as the limit of rescaled entropies along lattice approximations of the blowups of c. Existence is shown by proving a corresponding Shannon-McMillan theorem. We obtain a representation of h (c) (P) as a mixture of specific entropies along the tangent lines of c. As an application, the specific entropy along curves is used to refine Follmer and Ort's lower bound for the large deviations of the empirical field of an attractive Gibbs measure from its ergodic behaviour in the phase-transition regime.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Library of Congress Subject Headings (LCSH): | Random fields, Large deviations, Curves, Entropy (Information theory) | ||||
Journal or Publication Title: | Probability Theory and Related Fields | ||||
Publisher: | Springer | ||||
ISSN: | 0178-8051 | ||||
Official Date: | November 2008 | ||||
Dates: |
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Volume: | Volume 142 | ||||
Number: | Numbers 3-4 | ||||
Number of Pages: | 31 | ||||
Page Range: | pp. 443-473 | ||||
DOI: | 10.1007/s00440-007-0112-z | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Data sourced from Thomson Reuters' Web of Knowledge
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