{{See also|Probabilistic number theory}}
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.<ref>{{cite conference | last = Schwarz | first = W. | editor1-last = Grigelionis | editor1-first = B. | editor2-last = Kubilius | editor2-first = J. | editor3-last = Pragarauskas | editor3-first = H. | editor4-last = Statulevičius | editor4-first = V. | contribution = Some aspects of the development of probabilistic number theory | location = Vilnius | mr = 1649606 | pages = 661–701 | publisher = TEV | title = Probability theory and mathematical statistics: Proceedings of the 6th International Conference held in Vilnius, June 28–July 3, 1993 | year = 1994}}; see [https://books.google.com/books?id=9UMOvAsTXVkC&pg=PA674 p. 674]</ref>
The method was introduced in Jonas Kubilius's monograph ''Tikimybiniai metodai skaičių teorijoje'' (published in Lithuanian in 1959)<ref>{{cite web|url=http://old.mii.lt/?siteaction=pages.browse&page=istorija_skerus|title=MATEMATIKA LIETUVOS MOKSLŲ AKADEMIJOJE|accessdate=14 April 2018}}</ref> / ''Probabilistic Methods in the Theory of Numbers'' (published in English in 1964) .<ref>J.Kubilius {{Google books|2TEJAQAAQBAJ|Probabilistic methods in the Theory of Numbers}}</ref>
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."<ref>{{cite book |editor1-first=Eugenijus |editor1-last=Manstavičius |editor2-first=Fritz |editor2-last=Schweiger |title=Analytic and probabilistic methods in number theory |url=https://books.google.com/books?id=PewI8EsBTWEC |accessdate=2009-04-17 |series=New Trends in Probability and Statistics |volume=2 |year=1992 |publisher=VSP |location=Utrecht |isbn=978-90-6764-094-7 }}</ref>{{Rp|xi}}
==References== {{Reflist}}
==Further reading== * {{cite web | title=Selected publications of Professor Jonas Kubilius | url=http://www.mif.vu.lt/ttsk/bylos/ku/kpubla.html | publisher=Vilnius University | date=March 5, 2001 | accessdate=14 April 2018}} * {{cite web | title=Biography: Jonas Kubilius | url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Kubilius.html | website=www-history.mcs.st-andrews.ac.uk | accessdate=14 April 2018}}
Category:Number theory