Annales Mathématiques
Blaise Pascal
no. S2
Describability via ubiquity and eutaxy in Diophantine approximation
Arnaud Durand1
1 Laboratoire de Mathématiques d’Orsay Univ. Paris-Sud, CNRS Université Paris-Saclay 91405 Orsay, France
Annales mathématiques Blaise Pascal, Tome 22 (2015) no. S2, pp. 1-149.

We present a comprehensive framework for the study of the size and large intersection properties of limsup sets 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.

DOI : 10.5802/ambp.349
Classification : 11J82, 11J83, 28A78, 28A80, 60D05, 60G17, 60G51

Arnaud Durand 1

1 Laboratoire de Mathématiques d’Orsay Univ. Paris-Sud, CNRS Université Paris-Saclay 91405 Orsay, France 
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Arnaud Durand. Describability via ubiquity and eutaxy in Diophantine approximation. Annales mathématiques Blaise Pascal, Tome 22 (2015) no. S2, pp. 1-149. doi : 10.5802/ambp.349. https://ambp.centre-mersenne.org/articles/10.5802/ambp.349/

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