Documents

We find the limiting distributions for the maximal area of random
convex inscribed polygons and for minimal area of random convex circumscribed polygons whose vertices are distributed on the circumference with
almost arbitrary continuous density. These distributions belong to the
Weibull family. From this we deduce new limit theorems in the case when
the vertices of polygons have the uniform distribution on the ellipse. Some
similar theorems are formulated also for perimeters of inscribed and circumscribed polygons.
Translated title of the contributionLimit theorems for areas and perimeters of random inscribed and circumscribed polygons
Original languageRussian
Pages (from-to)200-213
JournalЗАПИСКИ НАУЧНЫХ СЕМИНАРОВ САНКТ-ПЕТЕРБУРГСКОГО ОТДЕЛЕНИЯ МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМ. В.А. СТЕКЛОВА РАН
Volume486
StatePublished - 13 Jan 2020

    Research areas

  • U$-max statistics, Weibull distribution, random perimete, random area, inscribed polygon

ID: 50521281