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A new proof of the dimension gap for the Gauss map.
- Source :
-
Mathematical Proceedings of the Cambridge Philosophical Society . Jan2022, Vol. 172 Issue 1, p43-71. 29p. - Publication Year :
- 2022
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GAUSS maps
*PROBABILITY measures
Subjects
Details
- Language :
- English
- ISSN :
- 03050041
- Volume :
- 172
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publication Type :
- Academic Journal
- Accession number :
- 154214451
- Full Text :
- https://doi.org/10.1017/S0305004121000104