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Large deviations for systems with non-uniform structure


Authors: Vaughn Climenhaga, Daniel J. Thompson and Kenichiro Yamamoto
Journal: Trans. Amer. Math. Soc. 369 (2017), 4167-4192
MSC (2010): Primary 37A50, 60F10, 37D35, 37D25, 37B10
DOI: https://doi.org/10.1090/tran/6786
Published electronically: January 9, 2017
MathSciNet review: 3624405
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Abstract | References | Similar Articles | Additional Information

Abstract: We use a weak Gibbs property and a weak form of specification to derive level-2 large deviations principles for symbolic systems equipped with a large class of reference measures. This has applications to a broad class of symbolic systems, including $ \beta $-shifts, $ S$-gap shifts, and their factors. A crucial step in our approach is to prove a `horseshoe theorem' for these systems.


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Additional Information

Vaughn Climenhaga
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204
Email: climenha@math.uh.edu

Daniel J. Thompson
Affiliation: Department of Mathematics, The Ohio State University, 100 Math Tower, 231 West 18th Avenue, Columbus, Ohio 43210
Email: thompson@math.osu.edu

Kenichiro Yamamoto
Affiliation: Department of General Education, Nagaoka University of Technology, Niigata 940-2188, Japan
Email: k_yamamoto@vos.nagaokaut.ac.jp

DOI: https://doi.org/10.1090/tran/6786
Received by editor(s): April 19, 2013
Received by editor(s) in revised form: June 12, 2015
Published electronically: January 9, 2017
Additional Notes: The first author was partially supported by NSF grant DMS-1362838
The second author was partially supported by NSF grants DMS-$1101576$ and DMS-$1259311$
Article copyright: © Copyright 2017 American Mathematical Society