title: Discretization of the parking problem
metadata.name: dc.contributor.author
metadata.value: Kryukov, Nikolai А.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-12-21T19:29:22Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-12-21T19:29:22Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Kryukov N. A. Discretization of the parking problem. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 4, pp. 662–677.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2020.408
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/21917
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The present work consider a natural discretization of Rényi’s so-called “parking problem”.
  Let l, n, i be integers satisfying l ≥ 2, n ≥ 0 and 0 ≤ i ≤ n − l. We place an open interval
  (i, i + l) in the segment [0, n] with i being a random variable taking values 0, 1, 2,...,n − l
  with equal probability for all n ≥ l. If n<l we say that the interval does not fit. After
  placing the first interval two free segments [0, i] and [i+ l, n] are formed and independently
  filled with the intervals of length l according to the same rule, etc. At the end of the filling
  process the distance between any two adjacent unit intervals is at most l−1. Let ξn,l denote
  the cumulative length of the intervals placed. The asymptotics behavior of expectations of
  the aforementioned random sequence have already been studied. This contribution has
  an aim to continue this investigation and establish the behavior of variances of the same
  sequence.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This study was supported by the Russian Foundation for Basic Research, 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 7 (65); 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.title
metadata.value: Discretization of the parking problem
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 662-677.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/21917/1/662-677.pdf
resources.format: Adobe PDF
resources.size: 340,96 kB