Pair Correlations and Random Walks on the Integers

Radhakrishnan Nair; Entesar Nasr

doi:10.1515/udt-2016-0008

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Pair Correlations and Random Walks on the Integers

Uniform distribution theory

Volume 11 (2016): Issue 1 (June 2016)

By: Radhakrishnan Nair and Entesar Nasr

Open Access

|Jan 2017

Abstract

The paper gives conditions for a sequence of fractional parts of real numbers ${({a_{n} x})}_{n = 1}^{\infty}$ $\left( {\{ a_n x\} } \right)_{n = 1}^\infty $ to satisfy a pair correlation estimate. Here x is a fixed nonzero real number and ${(a_{n})}_{n = 1}^{\infty}$ $\left( {a_n } \right)_{n = 1}^\infty $ is a random walk on the integers.

References

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Articles in this issue

DOI: https://doi.org/10.1515/udt-2016-0008 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 159 - 164

Submitted on: Mar 10, 2015

Accepted on: Mar 22, 2016

Published on: Jan 13, 2017

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

pair correlation,

random walks

Related subjects:

Mathematics,

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2017 Radhakrishnan Nair, Entesar Nasr, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 11 (2016): Issue 1 (June 2016)