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

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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
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of 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:	Date Event November 2008 Published
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

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