Indexing metadata

On the maximal length of arithmetic progressions


 
Dublin Core PKP Metadata Items Metadata for this Document
 
1. Title Title of document On the maximal length of arithmetic progressions
 
2. Creator Author's name, affiliation, country Minzhi Zhao; Zhejiang University; China
 
2. Creator Author's name, affiliation, country Huizeng Zhang; Hangzhou Normal University; China
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) arithmetic progression; Bernoulli sequence; limit distribution; Chen-Stein method
 
3. Subject Subject classification 60F05; 60C05
 
4. Description Abstract

This paper is a continuation of a paper by Benjamini, Yadin and Zeitouni's on maximal arithmetic progressions in random subsets. In this paper the asymptotic distributions of the maximal arithmetic progressions and arithmetic progressions modulo $n$ relative to an independent Bernoulli sequence with parameter $p$ are given. The errors are estimated by using the Chen-Stein method. Then the almost sure limit behaviour of these statistics is discussed. Our work extends the previous results and gives an affirmative answer to the conjecture raised at the end of that paper.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Supported by the Zhejiang Province education department scientific research project (Grant No. Y201225728),by NSFC (Grant No. 11101113 ) , by ZJNSF (Grant No. R6090034), and by NSFC(Grant No. 11001070).
 
7. Date (YYYY-MM-DD) 2013-08-31
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2018
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2018
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
15. Rights Copyright and permissions The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.

Summary of the Creative Commons Attribution License

You are free
  • to copy, distribute, display, and perform the work
  • to make derivative works
  • to make commercial use of the work
under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.