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Hausdorff dimension of limsup sets of random rectangles in products of regular spaces


Authors: Fredrik Ekström, Esa Järvenpää, Maarit Järvenpää and Ville Suomala
Journal: Proc. Amer. Math. Soc. 146 (2018), 2509-2521
MSC (2010): Primary 28A80, 60D05
DOI: https://doi.org/10.1090/proc/13920
Published electronically: February 16, 2018
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Abstract: The almost sure Hausdorff dimension of the limsup set of randomly distributed rectangles in a product of Ahlfors regular metric spaces is computed in terms of the singular value function of the rectangles.


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Additional Information

Fredrik Ekström
Affiliation: Department of Mathematical Sciences, P.O. Box 3000, 90014 University of Oulu, Finland
Email: fredrik.ekstrom@oulu.fi

Esa Järvenpää
Affiliation: Department of Mathematical Sciences, P.O. Box 3000, 90014 University of Oulu, Finland
Email: esa.jarvenpaa@oulu.fi

Maarit Järvenpää
Affiliation: Department of Mathematical Sciences, P.O. Box 3000, 90014 University of Oulu, Finland
Email: maarit.jarvenpaa@oulu.fi

Ville Suomala
Affiliation: Department of Mathematical Sciences, P.O. Box 3000, 90014 University of Oulu, Finland
Email: ville.suomala@oulu.fi

DOI: https://doi.org/10.1090/proc/13920
Received by editor(s): May 15, 2017
Received by editor(s) in revised form: July 24, 2017, and August 3, 2017
Published electronically: February 16, 2018
Additional Notes: We acknowledge the support of the Centre of Excellence in Analysis and Dynamics, funded by the Academy of Finland. We thank P. Mattila, S. Seuret, P. Shmerkin and J. Tyson for useful discussions, and the program Fractal Geometry and Dynamics, held at Institut Mittag–Leffler.
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2018 American Mathematical Society

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