JournalsdmVol. 27pp. 1015–1029

Variance bounds for disc-polygons

  • Ferenc Fodor

    Department of Geometry, Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary

  • Balázs Grünfelder

    University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary

  • Viktor Vígh

    Department of Geometry, Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary
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Abstract

We prove asymptotic lower bounds on the variance of the number of vertices and missed area of random disc-polygons in convex discs whose boundary is smooth. The established lower bounds are of the same order as the upper bounds proved previously in [F. Fodor and V. Vígh, J. Appl. Probab. 55, No. 4, 1143–1157 (2018; Zbl 1407.52004)].

Cite this article

Ferenc Fodor, Balázs Grünfelder, Viktor Vígh, Variance bounds for disc-polygons. Doc. Math. 27 (2022), pp. 1015–1029

DOI 10.4171/DM/891