On the average perimeter of the inscribed random polygon

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On the average perimeter of the inscribed random polygon. / Nikitin, Ya.Yu. ; Polevaya, T. A. .

In: Vestnik St. Petersburg University: Mathematics, Vol. 53, No. 1, 26.03.2020, p. 58-63.

Research output: Contribution to journal › Article › peer-review

Author

Nikitin, Ya.Yu. ; Polevaya, T. A. . / On the average perimeter of the inscribed random polygon. In: Vestnik St. Petersburg University: Mathematics. 2020 ; Vol. 53, No. 1. pp. 58-63.

BibTeX

@article{8853cc57e7474b91aa104b5593eb4e32,

title = "On the average perimeter of the inscribed random polygon",

abstract = "Assume that n independent uniformly distributed random points are set on the unit circle. Construct the convex random polygon with vertices in these points. What are the average area and the average perimeter of this polygon? Brown computed the average area several years ago. We compute the average perimeter and obtain quite similar expressions. We also discuss the rate of the convergence of this value to the limit and evaluate the average value of the sum of squares for the sides of the inscribed triangle.",

keywords = "периметр, U-статистика, равномерное распределение, random polygons, perimeter, convexity, uniform distribution, random polygon",

author = "Ya.Yu. Nikitin and Polevaya, {T. A.}",

note = "Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd.",

year = "2020",

month = mar,

day = "26",

doi = "10.1134/S1063454120010070",

language = "English",

volume = "53",

pages = "58--63",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - On the average perimeter of the inscribed random polygon

AU - Nikitin, Ya.Yu.

AU - Polevaya, T. A.

PY - 2020/3/26

Y1 - 2020/3/26

N2 - Assume that n independent uniformly distributed random points are set on the unit circle. Construct the convex random polygon with vertices in these points. What are the average area and the average perimeter of this polygon? Brown computed the average area several years ago. We compute the average perimeter and obtain quite similar expressions. We also discuss the rate of the convergence of this value to the limit and evaluate the average value of the sum of squares for the sides of the inscribed triangle.

AB - Assume that n independent uniformly distributed random points are set on the unit circle. Construct the convex random polygon with vertices in these points. What are the average area and the average perimeter of this polygon? Brown computed the average area several years ago. We compute the average perimeter and obtain quite similar expressions. We also discuss the rate of the convergence of this value to the limit and evaluate the average value of the sum of squares for the sides of the inscribed triangle.

KW - периметр, U-статистика, равномерное распределение

KW - random polygons

KW - perimeter

KW - convexity

KW - uniform distribution

KW - random polygon

UR - https://link.springer.com/article/10.1134/S1063454120010070

UR - http://www.scopus.com/inward/record.url?scp=85082581958&partnerID=8YFLogxK

U2 - 10.1134/S1063454120010070

DO - 10.1134/S1063454120010070

M3 - Article

VL - 53

SP - 58

EP - 63

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -

ID: 52028477