A new proof of the dimension gap for the Gauss map
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In , Kifer, Peres and Weiss showed that the Bernoulli measures for the Gauss map T(x)=1/x mod 1 satisfy a 'dimension gap' meaning that for some c > 0, supp dim μp < 1-c, where μp denotes the (pushforward) Bernoulli measure for the countable probability vector p. In this paper we propose a new proof of the dimension gap. By using tools from thermodynamic formalism we show that the problem reduces to obtaining uniform lower bounds on the asymptotic variance of a class of potentials.
Jurga , N 2021 , ' A new proof of the dimension gap for the Gauss map ' , Mathematical Proceedings of the Cambridge Philosophical Society , vol. FirstView . https://doi.org/10.1017/S0305004121000104
Mathematical Proceedings of the Cambridge Philosophical Society
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the final published version of the work, which was originally published at https://doi.org/10.1017/S0305004121000104.
DescriptionFunding: This paper was written while the author was supported by a Leverhulme Trust Research Project Grant (RF-2016-194).
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