Kubilius model
In mathematics, the Kubilius model relies on a clarification and extension of a finite probability space on which the behaviour of additive arithmetic functions can be modeled by sum of independent random variables.[1]
The method was introduced in Jonas Kubilius's monograph Tikimybiniai metodai skaičių teorijoje (published in Lithuanian in 1959)[2] / Probabilistic Methods in the Theory of Numbers (published in English in 1964) .[3]
Eugenijus Manstavičius and Fritz Schweiger wrote about Kubilius's work in 1992, "the most impressive work has been done on the statistical theory of arithmetic functions which almost created a new research area called Probabilistic Number Theory. A monograph (Probabilistic Methods in the Theory of Numbers) devoted to this topic was translated into English in 1964 and became very influential."[4]:xi
References
- ↑ Schwarz, W. (1994). "Probability theory and mathematical statistics: Proceedings of the 6th International Conference held in Vilnius, June 28–July 3, 1993". in Grigelionis, B.; Kubilius, J.; Pragarauskas, H. et al.. Vilnius: TEV. pp. 661–701.; see p. 674
- ↑ "MATEMATIKA LIETUVOS MOKSLŲ AKADEMIJOJE". http://old.mii.lt/?siteaction=pages.browse&page=istorija_skerus. Retrieved 14 April 2018.
- ↑ J.Kubilius Probabilistic methods in the Theory of Numbers at Google Books
- ↑ Manstavičius, Eugenijus; Schweiger, Fritz, eds (1992). Analytic and probabilistic methods in number theory. New Trends in Probability and Statistics. 2. Utrecht: VSP. ISBN 978-90-6764-094-7. https://books.google.com/books?id=PewI8EsBTWEC. Retrieved 2009-04-17.
Further reading
- "Selected publications of Professor Jonas Kubilius". Vilnius University. March 5, 2001. http://www.mif.vu.lt/ttsk/bylos/ku/kpubla.html. Retrieved 14 April 2018.
- "Biography: Jonas Kubilius". http://www-history.mcs.st-andrews.ac.uk/Biographies/Kubilius.html. Retrieved 14 April 2018.
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