Variance bounds for disc-polygons

2021/11/02 by Ferenc Fodor, Fodor, Ferenc, Balázs Grünfelder +3 · 1 citation
Mathematics · #52A22 #60D05 #FOS: Mathematics #Geometry and complex manifolds #Metric Geometry (math.MG) #Point processes and geometric inequalities #Probability (math.PR)

paper · doi:10.48550/arxiv.2111.01725

openalex publication_date 2021/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 C₊² smooth. The established lower bounds are of the same order as the upper bounds proved previously by Fodor and V'ıgh (2018).

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