Geodesic
Asymptotic normality in a discrete analog of the parking problem
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 9-36 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article, the authors study the behavior of the central moments of higher orders in a discrete version of the “parking problem”. For these moments, asymptotic behavior is obtained when the length of the filled segment increases indefinitely. This made it possible to prove the asymptotic normality of the total length of the allocated intervals of length $ l $ on an interval of length $ n $ for any fixed $ l \ge 2 $, when $ n $ increases unboundedly. 
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S. M. Ananjevskii; N. A. Kryukov. Asymptotic normality in a discrete analog of the parking problem. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 9-36. http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a1/

[1] A. Rényi, “On a one-dimensional problem concerning space-filling”, Publ. Math. Inst. Hungarian Acad. Scie., 3 (1958), 109–127 | MR

[2] A. Dvoretzky, H. Robbins, “On the “parking” problem”, Publ. Math. Inst. Hungarian Acad. Scie., 9 (1964), 209–226 | MR

[3] R. G. Pinsky, Problems from the Discrete to the Continuous, v. 3, Springer International Publishing Switzerland, 2014, 21–34 | DOI | MR

[4] S. M. Ananevskii, N. A. Kryukov, “Zadacha ob egoistichnoi parkovke”, Vestnik Sankt-Peterburgskogo universiteta. Matematika. Mekhanika. Astronomiya, 5 (63):4 (2018), 549–555 | DOI

[5] S. M. Ananevskii, N. A. Kryukov, “Ob asimptoticheskoi normalnosti v odnom obobschenii zadachi Reni”, Vestnik Sankt-Peterburgskogo universiteta. Matematika. Mekhanika. Astronomiya, 6 (64):3 (2019), 353–362 | DOI | Zbl

[6] M. P. Clay, N. J. Simanyi, Rényi's parking problem revisited, 29 Dec. 2014, arXiv: 1406.1781v1 [math.PR] | MR

[7] L. Geri, The Page-Rényi parking process, 28 Nov.2014, arXiv: 1411.8002v1 [math.PR] | MR

[8] S. M. Ananevskii, “Nekotorye obobscheniya zadachi o “parkovke””, Vestnik Sankt-Peterburgskogo universiteta. Matematika. Mekhanika. Astronomiya, 3 (61):4 (2016), 525–532 | DOI

[9] S. M. Ananevskii, “Zadacha parkovki dlya otrezkov razlichnoi dliny”, Veroyatnost i statistika, Zap. nauchn. semin. POMI, 228, 1996, 16–23

[10] A. B. Ilєnko, V. V. Fatenko, “Uzagalnennya zadachi Renï pro parkuvannya”, Naukovi visti NTUU “KPI”: mizhnarodnii naukovo-tekhnichnii zhurnal, 2017, no. 4(114), 54–60

[11] N. A. Kryukov, “Diskretizatsiya zadachi o parkovke”, Vestnik Sankt-Peterburgskogo universiteta. Matematika. Mekhanika. Astronomiya, 7(65):4 (to appear) | MR

[12] P. Billingsley, Probability and Measure, Third Edition, A Wiley–Interscience Publication, John Wiley Sons, New York, 1985 | MR