{"title":"A Continuous Version of the Selfish Parking Problem","authors":"S. M. Ananjevskii, A. P. Chen","doi":"10.1134/s1063454124010023","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A new model of the random filling of a segment of large length with intervals of smaller length is studied. A new statement of the problem is considered. A model in which unit intervals are placed on a segment only if the segment being filled has a length of at least 2 is considered. The position of the interval to be placed is subject to a uniform distribution law. The behavior of the average number of intervals placed is studied depending on the length of the segment to be filled. An exact expression is obtained for the analog of Rényi’s constant.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik St Petersburg University-Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1063454124010023","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
A new model of the random filling of a segment of large length with intervals of smaller length is studied. A new statement of the problem is considered. A model in which unit intervals are placed on a segment only if the segment being filled has a length of at least 2 is considered. The position of the interval to be placed is subject to a uniform distribution law. The behavior of the average number of intervals placed is studied depending on the length of the segment to be filled. An exact expression is obtained for the analog of Rényi’s constant.
期刊介绍：
Vestnik St. Petersburg University, Mathematics is a journal that publishes original contributions in all areas of fundamental and applied mathematics. It is the prime outlet for the findings of scientists from the Faculty of Mathematics and Mechanics of St. Petersburg State University. Articles of the journal cover the major areas of fundamental and applied mathematics. The following are the main subject headings: Mathematical Analysis; Higher Algebra and Numbers Theory; Higher Geometry; Differential Equations; Mathematical Physics; Computational Mathematics and Numerical Analysis; Statistical Simulation; Theoretical Cybernetics; Game Theory; Operations Research; Theory of Probability and Mathematical Statistics, and Mathematical Problems of Mechanics and Astronomy.
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