title: Asymptotic normality in the problem of selfish parking
metadata.name: dc.contributor.author
metadata.value: Ananjevskii, Sergey M.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Kryukov, Nikolay A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-12-06T11:28:06Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-12-06T11:28:06Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ananjevskii S.M., Kryukov N.A. Asymptotic normality in the problem of selfish parking. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 4, pp. 592–607.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.405
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16742
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In the present work we continue to study one of the models of a discrete analogue of the
  Renyi problem, known as the “parking problem”. Let n, i be integers satisfying n   0 and
  0   i   n−1. We place an open interval (i, i+1) in the segment [0, n] with i being a random
  variable taking values 0, 1, 2, . . . , n−1 with equal probability for all n   2. If n < 2 we say
  that the interval does not fit. After placing the first interval two free segments [0, i] and
  [i + 1, n] are formed and independently filled with the intervals of unit length according to
  the same rule, etc. At the end of the filling process the distance between any two adjacent
  unit intervals is at most 1. Let Xn denote the number of the unit intervals placed. In
  the previous work of the authors, published in 2018, the asymptotic behavior of the first
  moments of the random variable Xn was studied. In contrast to the classical case, the exact
  expressions were obtained for the expectation, variance, and third central moments. In this
  paper the asymptotic behavior of all central moments of the random variable Xn is studied
  and the asymptotic normality is proved for Xn.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The article was prepared with the financial support of the Russian Foundation for Basic Research (RFBR), project No. 18-01-00393.
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 6 (64); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: random filling
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: discrete “parking” problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: asymptotic behavior of moments
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: asymptotic normality
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Asymptotic normality in the problem of selfish parking
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 592-607.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16742/1/592-607.pdf
resources.format: Adobe PDF
resources.size: 318,34 kB