Seminar

Hausdorff dimensions and hitting probabilities of random covering sets

Fractal Geometry and Dynamics

28 September 14:00 - 14:50

Li Bing - South China University of Technology

The Dvoretzky random covering problem is to find the conditions for which almost surely every point on the circle is covered infinitely many times by a sequence of random intervals with decreasing lengths and random initial points (an i.i.d. sequence of random variables uniformly distributed on the circle). It has drawn a lot of interest of many mathematicians for the last decades and the sizes of the random covering sets have been widely studied. The Hausdorff dimensions and hitting probabilities of random covering sets will be given in the talk. The covering setting also was generalized to many different cases, for example, covering the torus with rectangles or open sets, or even just Lebesgue measure sets, or balls with singular distributions, some recent related results will be surveyed.
Organizers
Kenneth J. Falconer
University of St Andrews
Maarit Järvenpää
University of Oulu
Antti Kupiainen
University of Helsinki
Francois Ledrappier
University of Notre Dame
Pertti Mattila
University of Helsinki

Program
Contact

Maarit Järvenpää

maarit.jarvenpaa@oulu.fi

Other
information

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