Uniform distribution theory is the study of point sets and sequences having a uniform
distribution. Uniform distribution theory is important in modeling and simulation,
and especially in so-called Monte Carlo and
quasi-Monte Carlo methods, and seeks to
characterize and construct well distributed point sets
and sequences.
Kakutani partitions of the unit interval give a deterministic example. Choosing one point
in the interior of each interval
produces finite point sets whose relative frequencies
in subintervals approach the corresponding lengths (Smilansky
2020).
See also
Hammersley Point Set,
Monte Carlo Method,
Net,
Quasi-Monte Carlo Method,
Quasirandom
Sequence,
Uniform Distribution
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References
Drmota, M. and Tichy, R. F. Sequences, Discrepancies and Applications. New York: Springer-Verlag, 1997.Hellekalek,
P. and Larcher, G. (Eds.). Random
and Quasi-Random Point Sets. New York: Springer-Verlag, 1998.Kuipers,
L. and Niederreiter, H. Uniform
Distribution of Sequences. New York: Wiley, 1974.Smilansky,
Y. "Uniform Distribution of Kakutani Partitions Generated by Substitution Schemes."
Israel J. Math. 240, 667-710, 2020. https://doi.org/10.1007/s11856-020-2075-z.Referenced
on Wolfram|Alpha
Uniform Distribution Theory
Cite this as:
Weisstein, Eric W. "Uniform Distribution Theory."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/UniformDistributionTheory.html
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