Abstract
We prove asymptotic formulas for the expectation of the vertex number and missed area of uniform random disc-polygons in convex disc-polygons. Our statements are the r-convex analogues of the classical results of Rényi and Sulanke [10] about random polygons in convex polygons.
Funding Statement
F. Fodor was supported by the National Research, Development and Innovation Office – NKFIH K134814 grant. P. Kevei was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. V. Vígh was supported by the National Research, Development and Innovation Office – NKFIH FK135392 grant. This research was supported by grant NKFIH-1279-2/2020 of the Ministry for Innovation and Technology, Hungary.
Dedication
Dedicated to the memory of our dear friend and colleague Gabriella Ágnes Vas.
Citation
Ferenc Fodor. Péter Kevei. Viktor Vígh. "On random disc-polygons in a disc-polygon." Electron. Commun. Probab. 28 1 - 11, 2023. https://doi.org/10.1214/23-ECP515
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