Kubilius model

{{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.{{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]

The method was introduced in Jonas Kubilius's monograph Tikimybiniai metodai skaičių teorijoje (published in Lithuanian in 1959){{cite web|url=http://old.mii.lt/?siteaction=pages.browse&page=istorija_skerus|title=MATEMATIKA LIETUVOS MOKSLŲ AKADEMIJOJE|accessdate=14 April 2018}} / Probabilistic Methods in the Theory of Numbers (published in English in 1964) .J.Kubilius {{Google books|2TEJAQAAQBAJ|Probabilistic methods in the Theory of Numbers}}

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."{{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 }}{{Rp|xi}}