<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>For sequences sufficiently close to (<italic>a</italic> log <italic>n</italic>), with an arbitrary real constant <italic>a</italic>, this note describes the precise asymptotics of the associated empirical distributions modulo one, with respect to the Kantorovich metric as well as a discrepancy-style metric. In particular, the note demonstrates how these asymptotics depend on <italic>a</italic> in a delicate, discontinuous way. The results strengthen and complement known facts in the literature.</p>
</abstract>

For sequences sufficiently close to (a log n), with an arbitrary real constant a, this note describes the precise asymptotics of the associated empirical distributions modulo one, with respect to the Kantorovich metric as well as a discrepancy-style metric. In particular, the note demonstrates how these asymptotics depend on a in a delicate, discontinuous way. The results strengthen and complement known facts in the literature.

A Note on the Distributions of (log <italic>n</italic>)mod 1

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A Note on the Distributions of (log )mod 1

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For sequences sufficiently close to (a log n), with an arbitrary real constant a, this note describes the precise asymptotics of the associated empirical...

A Note on the Distributions of (log n)mod 1

Published Online: Dec 12, 2022

Page range: 77 - 100

Received: Apr 29, 2022

Accepted: Jun 21, 2022

DOI: https://doi.org/10.2478/udt-2022-0013

Keywords
Slowly changing sequence, distribution modulo one, Kantorovich metric, discrepancy

© 2022 Arno Berger, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A Note on the Distributions of (log n)mod 1

Published Online: Dec 12, 2022

Page range: 77 - 100

Received: Apr 29, 2022

Accepted: Jun 21, 2022

DOI: https://doi.org/10.2478/udt-2022-0013

KeywordsSlowly changing sequence, distribution modulo one, Kantorovich metric, discrepancy

© 2022 Arno Berger, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Slowly changing sequence, distribution modulo one, Kantorovich metric, discrepancy