Hitting probabilities of random covering sets in tori and metric spaces

2015/10/22 by Järvenpää, Esa, Järvenpää, Maarit, Koivusalo, Henna +3 · 1 citation
#Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1510.06630

Abstract

We provide sharp lower and upper bounds for the Hausdorff dimension of the intersection of a typical random covering set with a fixed analytic set both in Ahlfors regular metric spaces and in the d-dimensional torus. In metric spaces, we consider covering sets generated by balls and, in the torus, we deal with general analytic generating sets.

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