Random covering by rectangles on self-similar carpets

2025/10/06 by Edouard Daviaud, Daviaud, E · 2 citations
Mathematics · #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2510.04879

Abstract

In this article, given a base-b self-similar set K, we study the random covering of K by horizontal or vertical rectangles, with respect to the Alfhors-regular measure on K, and the rectangular shrinking target problem on K.

Citations

• Rectangular Shrinking Targets on Self-Similar Carpets
• Intrinsic Diophantine Approximation for overlapping iterated function systems
• On the Hausdorff measure of shrinking target sets on self-conformal sets
• Dimensions of random covering sets in Riemann manifolds
• Dimension via Waiting time and Recurrence

Cited by

• Twisted Diophantine approximation for matrix transformations of tori
• Rectangular Shrinking Targets on Self-Similar Carpets

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