A new proof of the dimension gap for the Gauss map

N. Jurga*

*Corresponding author for this work

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In [4], 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.
Original languageEnglish
Number of pages29
JournalMathematical Proceedings of the Cambridge Philosophical Society
Publication statusPublished - 15 Jun 2021


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