title: Limit theorems for generalized perimeters of random inscribed polygons. II
metadata.name: dc.contributor.author
metadata.value: Simarova, Ekaterina N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-05-04T19:25:09Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-05-04T19:25:09Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Simarova E.N. Limit theorems for generalized perimeters of random inscribed polygons. II. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 1, pp. 101–110.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.109
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/28437
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Lao and Mayer (2008) recently developed the theory of U-max statistics, where instead of
  the usual sums over subsets, the maximum of the kernel is considered. Such statistics often
  appear in stochastic geometry. Examples include the greatest distance between random
  points in a ball, the maximum diameter of a random polygon, the largest scalar product
  in a sample of points, etc. Their limit distributions are related to distribution of extreme
  values. This is the second article devoted to the study of the generalized perimeter of a
  polygon and the limit behavior of the U-max statistics associated with the generalized perimeter. Here we consider the case when the parameter y, arising in the definition of the
  generalized perimeter, is greater than 1. The problems that arise in the applied method in
  this case are described. The results of theorems on limit behavior in the case of a triangle
  are refined.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work is supported by Ministry of Science and Higher Education of the Russian Federation
  (agreement No. 075-15-2019-1619), and by joint RFBR-DFG (grant No. 20-51-12004).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 8 (66); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: U-max statistics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: limit behavior
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: uniform distribution on a circle
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: the sum of the degrees of the sides of the polygon
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Limit theorems for generalized perimeters of random inscribed polygons. II
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 101-110.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/28437/1/101-110.pdf
resources.format: Adobe PDF
resources.size: 305,86 kB