Describability via ubiquity and eutaxy in Diophantine approximation

Abstract : We present a comprehensive framework for the study of the size and large intersection properties of sets of limsup type that arise naturally in Diophantine approximation and multifractal analysis. This setting encompasses the classical ubiquity techniques, as well as the mass and the large intersection transference principles, thereby leading to a thorough description of the properties in terms of Hausdorff measures and large intersection classes associated with general gauge functions. The sets issued from eutaxic sequences of points and optimal regular systems may naturally be described within this framework. The discussed applications include the classical homogeneous and inhomogeneous approximation, the approximation by algebraic numbers, the approximation by fractional parts, the study of uniform and Poisson random coverings, and the multifractal analysis of Lévy processes.
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https://hal.archives-ouvertes.fr/hal-01143640
Contributor : Arnaud Durand <>
Submitted on : Sunday, April 19, 2015 - 3:18:32 AM
Last modification on : Thursday, January 11, 2018 - 6:12:19 AM
Long-term archiving on : Monday, September 14, 2015 - 10:35:39 AM

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  • HAL Id : hal-01143640, version 1
  • ARXIV : 1504.04984

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Arnaud Durand. Describability via ubiquity and eutaxy in Diophantine approximation. 2015. ⟨hal-01143640⟩

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