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2013 On the maximal length of arithmetic progressions
Minzhi Zhao, Huizeng Zhang
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Electron. J. Probab. 18: 1-21 (2013). DOI: 10.1214/EJP.v18-2018


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.


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Minzhi Zhao. Huizeng Zhang. "On the maximal length of arithmetic progressions." Electron. J. Probab. 18 1 - 21, 2013.


Accepted: 31 August 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1285.60022
MathSciNet: MR3101645
Digital Object Identifier: 10.1214/EJP.v18-2018

Primary: 60F05
Secondary: 60C05

Keywords: arithmetic progression , Bernoulli sequence , Chen-Stein method , limit distribution

Vol.18 • 2013
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