Characterizing Benford's Law in Linear Systems

• Author / Creator

  Eshun, Gideon

• 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.

• Subjects / Keywords

  • Linear
  • Systems
  • Benford

• Graduation date

  Fall 2014

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3Q81515F

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.