Abstract
A new definition of uniformly distributed sequences based on the entropy is presented. A description of a set of points via density functions using the Maximum Entropy Principle is given and an entropic measure of uniformity is proposed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Weyl H., Über die Gleichverteilung von Zahlen mod. Eins’, Math. Ann. 77, 313–352, (1916).
Sobol I.M., Punkte, die einen mehrdimensionalen Würfel gleichmässig ausfüllen’, Bericht 51, A.G.T. University of Kaiserslautern, (1991).
Kuipers L., Niederreiter H., Uniform Distribution of Sequences’, Wiley & Sons, (1974).
Reif F., Fundamentals of Statistical and Thermal Physics’,Mc Graw-Hill, (1965).
Jaynes E.T., Information Theory and Statistical Mechanics’, Phys. Rev. 106 (4), 620630, (1957).
Drabld D.A., Carlsson A.E. and Fedders P.A., Applications of Maximum Entropy to Condensed Matter Physics’, in J. Skilling (ed.), Maximum Entropy and Bayesian Methods, Kluwer, Dordrecht, (1989).
Aliaga J., Gruver J.L. and Proto A.N., `Generalized Bloch equations for time-dependent N-level systems’, Phys. Lett. A 153, 317–320, (1991).
Widder D.V., The Laplace Transform’, Princeton U. P., Princeton, (1946).
Mead L.R. and Papanicolaou N., Maximum entropy in the problem of moments’, J. Math. Phys. 25 (8), 2404–2417, (1984).
Mohammad-Djafari A., A Matlab Program to calculate the Maximum Entropy Distributions’, Proc of the 10th Int MaxEnt Workshop, Laramie, Wyoming, published in Maximum-entropy and Bayesian Methods, T.W. Grandy ed., (1990).
Bergström V., Einige Bemerkungen zur Theorie der diophantischen Approximationen’, Fysiogr. Sälsk. Lund. Förh. 6, 1–19, (1936).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Giuliani, D., Gruver, J.L. (1993). Uniformly Distributed Sequences and the Maximum Entropy Principle. In: Mohammad-Djafari, A., Demoment, G. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 53. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2217-9_16
Download citation
DOI: https://doi.org/10.1007/978-94-017-2217-9_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4272-9
Online ISBN: 978-94-017-2217-9
eBook Packages: Springer Book Archive