arXiv subjects

Édouard Daviaud

Publications and source records attributed to Édouard Daviaud.

2 recordsLinked to original sources

arXiv2022

Extraction of optimal subsequences of sequence of balls, and application to optimality estimates of mass transference principles

In this article, we prove that from any sequence of balls whose associated limsup set has full $μ$-measure, one can extract a well-distributed subsequence of balls. From this, we deduce the optimality of various lower bounds for the Hausdorff dimension of limsup sets of balls obtained by mass transference principles. We also establish a version of Borel-Cantelli divergence lemma particulary suited for limsup set generated by balls. This lemma is very similar to the one proved by Bersnevich and Velani but the measure is not assumed ot be doubling.

math.MG↗

arXiv2021

An anisotropic inhomogeneous ubiquity Theorem

Recently, mass transference principles in metric number theory extend towards two direction. On one hand, the shape of the approximating sets can be taken of various shape, balls, rectangles or even general open sets (one refers to some results of Rams and Koivusalo regarding this last example) when the ambient measure is Lebesgue, on the other hand, progress have been made to understand what can be said when the ambient measure is changed. For instance some computation in the case of a self-similar measure with open set condition have been made by Barral and Seuret. This article mixes the two approaches and presents a ubiquity theorem which handles the case where the approximating sets are rectangles and the measure is quasi-Bernoulli, but fully supported.

math.MG↗