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Non-uniqueness for specifications in $\ell ^{2+\unicode[STIX]{x1D716}}$

Published online by Cambridge University Press:  20 March 2017

NOAM BERGER ,
CHRISTOPHER HOFFMAN  and
VLADAS SIDORAVICIUS
NOAM BERGER
Affiliation:
Department of Mathematics, Technische Universität München, Boltzmannstrasse 3, 85748 Garching, Germany Department of Mathematics, the Hebrew University of Jerusalem, Israel
CHRISTOPHER HOFFMAN
Affiliation:
Department of Mathematics, Box #354350, University of Washington, Seattle, WA 98195-4350, USA
VLADAS SIDORAVICIUS
Affiliation:
Courant Institute of Mathematical Sciences, NYU, New York, USA NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, Shanghai, China Cemaden, São José dos Campos, Brasil
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Abstract

For every $p>2$, we construct a regular and continuous specification ($g$-function), which has a variation sequence that is in $\ell ^{p}$ and which admits multiple Gibbs measures. Combined with a result of Johansson and Öberg [Square summability of variations of $g$-functions and uniqueness in $g$-measures. Math. Res. Lett.10(5–6) (2003), 587–601], this determines the optimal modulus of continuity for a specification which admits multiple Gibbs measures.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 4 , June 2018 , pp. 1342 - 1352
Copyright
© Cambridge University Press, 2017 

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