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Permanent link (DOI): https://doi.org/10.7939/R3Q81515F

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Characterizing Benford's Law in Linear Systems Open Access

Descriptions

Other title
Subject/Keyword
Linear
Benford
Systems
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Eshun, Gideon
Supervisor and department
Berger, Arno (Mathematical and Statistical Sciences)
Examining committee member and department
Wolgar, Eric (Mathematical and Statistical Sciences)
Berger, Arno (Mathematical and Statistical Sciences)
Byron, Schmuland (Mathematical and Statistical Sciences)
Li, Micheal (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematical Physics
Date accepted
2014-07-29T14:09:21Z
Graduation date
2014-11
Degree
Master of Science
Degree level
Master's
Abstract
We study the widespread logarithmic distribution of first significant digits and significands of data sets (referred to as Benford’s Law ) in the context of dynamical systems. Using recent tools and conditions under which a recursively defined sequence is Benford via the classical theory of uniform distribution modulo one, this study derives a necessary and sufficient condition (“nonresonant spectrum”) on A ∈ R d×d for every sequence (y ⊤ A n x) n∈N , with arbitrary x, y ∈ R d , emanating from the difference equation x n = Ax n−1 , to be Benford or terminating. This result in turn is used to also show that the function t → y ⊤ e tA x arising from the differential equation x(t)= Ax(t) is either Benford or identically zero for t ≥ 0. The results generalize and unify already known facts for one- and higher-dimensional systems.
Language
English
DOI
doi:10.7939/R3Q81515F
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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