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{{Short description|Soviet mathematician (1915–1972)}}
[[File:Linnik.jpg|200px|thumb|right|Yuri V. Linnik]]
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'''Yuri Vladimirovich Linnik''' ({{lang-ru|Ю́рий Влади́мирович Ли́нник}}; January 8, 1915 – June 30, 1972) was a [[Soviet Union|Soviet]] [[mathematician]] active in [[number theory]], [[probability theory]] and [[mathematical statistics]].


{{Infobox scientist
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Linnik was born in [[Bila Tserkva]], in present-day [[Ukraine]]. He went to [[St Petersburg University]] where his supervisor was Vladimir Tartakovski, and later worked at that university and the [[Steklov Institute of Mathematics|Steklov Institute]]. He was a member of the [[Russian Academy of Sciences]], as was his father, Vladimir Pavlovich Linnik. He was awarded both [[USSR State Prize|State]] and [[Lenin Prize]]s. He died in [[Leningrad]].<ref>{{Citation|mr=0421941|last1=Faddeyev|first1=D. K.|last2=Lozinsky|first2=S. M.|last3=Malyshev|first3=A. V.|title=Yuri V. Linnik (1915&ndash;1972): a biographical note|journal=Acta Arith.|volume=27|year=1975|pages=1&ndash;2|postscript=.|doi=10.4064/aa-27-1-1-2|doi-access=free}}</ref>
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| birth_name = Yuri Vladimirovich Linnik
| birth_date = {{birth date|1915|01|8}}
| birth_place = [[Bila Tserkva]], [[Russian Empire]]
| death_date = {{death date and age|1972|06|30|1915|01|8}}
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'''Yuri Vladimirovich Linnik''' ({{lang-ru|Ю́рий Влади́мирович Ли́нник}}; January 8, 1915 – June 30, 1972) was a Soviet mathematician active in [[number theory]], [[probability theory]] and [[mathematical statistics]].

== Biography ==
⚫
Linnik was born in [[Bila Tserkva]], in present-day [[Ukraine]]. He went to [[Saint Petersburg State University|Saint Petersburg University]] where his supervisor was Vladimir Tartakovsky, and later worked at that university and the [[Steklov Institute of Mathematics|Steklov Institute]]. He was a member of the [[Academy of Sciences of the Soviet Union]], as was his father, Vladimir Pavlovich Linnik. He was awarded both [[USSR State Prize|Stalin]] and [[Lenin Prize]]s. He died in [[Saint Petersburg|Leningrad]].<ref>{{Citation|mr=0421941|last1=Faddeyev|first1=D. K.|last2=Lozinsky|first2=S. M.|last3=Malyshev|first3=A. V.|title=Yuri V. Linnik (1915&ndash;1972): a biographical note|journal=Acta Arith.|volume=27|year=1975|pages=1&ndash;2|postscript=.|doi=10.4064/aa-27-1-1-2|doi-access=free}}</ref>


==Work in number theory==
==Work in number theory==
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* The [[large sieve]] (which turned out to be extremely influential).
* The [[large sieve]] (which turned out to be extremely influential).
* An elementary proof of the [[Waring's problem|Hilbert-Waring theorem]]; see also [[Schnirelmann density]].
* An elementary proof of the [[Waring's problem|Hilbert-Waring theorem]]; see also [[Schnirelmann density]].
* The Linnik ergodic method, see {{harvtxt|Linnik|1968}}, which allowed him to study the distribution properties of the representations of integers by integral ternary [[quadratic forms]].<ref>{{Citation|last=Michel|first=Ph.|first2=A.|last2=Venkatesh|chapter= Equidistribution, L-functions and ergodic theory: on some problems of Yu. V. Linnik|title=Proceedings of ICM 2006|volume=2|publisher=Eur. Math. Soc.|location=Zurich|year=2006|pages=421&ndash;457}}</ref>
* The Linnik ergodic method, see {{harvtxt|Linnik|1968}}, which allowed him to study the distribution properties of the representations of integers by integral ternary [[Quadratic form|quadratic forms]].<ref>{{Citation|last=Michel|first=Ph.|first2=A.|last2=Venkatesh|chapter= Equidistribution, L-functions and ergodic theory: on some problems of Yu. V. Linnik|title=Proceedings of ICM 2006|volume=2|publisher=Eur. Math. Soc.|location=Zurich|year=2006|pages=421&ndash;457}}</ref>


==Work in probability theory and statistics==
==Work in probability theory and statistics==
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===Infinitely divisible distributions===
===Infinitely divisible distributions===


Linnik obtained numerous results concerning [[infinite divisibility (probability)|infinitely divisible distributions]].<ref>{{Citation|mr=1150561|last=Ibragimov|first=I. A.|title=Yu. V. Linnik. Some of his work from the 1950s|journal=St. Petersburg Math. J.|volume=3|year=1992|issue=3|pages=687&ndash;696|postscript=.}}</ref> In particular, he proved the following generalisation of [[Cramér’s decomposition theorem|Cramér's theorem]]: any divisor of a convolution of Gaussian and Poisson random variables is also a convolution of Gaussian and Poisson.
Linnik obtained numerous results concerning [[infinite divisibility (probability)|infinitely divisible distributions]].<ref>{{Citation|mr=1150561|last=Ibragimov|first=I. A.|title=Yu. V. Linnik. Some of his work from the 1950s|journal=St. Petersburg Math. J.|volume=3|year=1992|issue=3|pages=687&ndash;696|postscript=.}}</ref> In particular, he proved the following generalisation of [[Cramér's decomposition theorem|Cramér's theorem]]: any divisor of a convolution of Gaussian and Poisson random variables is also a convolution of Gaussian and Poisson.


He has also coauthored the book {{harvtxt|Linnik|Ostrovskii|1977}} on the arithmetics of infinitely divisible distributions.
He has also coauthored the book {{harvtxt|Linnik|Ostrovskii|1977}} on the arithmetics of infinitely divisible distributions.
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[[Category:1972 deaths]]
[[Category:1972 deaths]]
[[Category:20th-century Russian mathematicians]]
[[Category:20th-century Russian mathematicians]]
[[Category:Soviet mathematicians]]
[[Category:People from Bila Tserkva]]
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[[Category:Number theorists]]
[[Category:Full Members of the USSR Academy of Sciences]]
[[Category:Full Members of the USSR Academy of Sciences]]
[[Category:Members of the Royal Swedish Academy of Sciences]]
[[Category:Saint Petersburg State University alumni]]
[[Category:Heroes of Socialist Labour]]
[[Category:Heroes of Socialist Labour]]
[[Category:Recipients of the Stalin Prize]]
[[Category:Recipients of the Lenin Prize]]
[[Category:Recipients of the Order of the Badge of Honour]]
[[Category:Recipients of the Order of Lenin]]
[[Category:Recipients of the Order of the Red Banner of Labour]]
[[Category:Mathematical statisticians]]
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[[Category:Number theorists]]
[[Category:Russian statisticians]]
[[Category:Russian statisticians]]
[[Category:Soviet mathematicians]]
[[Category:Russian scientists]]

Latest revision as of 16:41, 31 October 2023

Yuri Linnik
Born
Yuri Vladimirovich Linnik

(1915-01-08)January 8, 1915
Bila Tserkva, Russian Empire
DiedJune 30, 1972(1972-06-30) (aged 57)
Leningrad, Soviet Union
NationalityRussian
Alma materSaint Petersburg University
Steklov Institute
Scientific career
FieldsMathematics
InstitutionsSaint Petersburg University

Yuri Vladimirovich Linnik (Russian: Ю́рий Влади́мирович Ли́нник; January 8, 1915 – June 30, 1972) was a Soviet mathematician active in number theory, probability theory and mathematical statistics.

Biography

[edit]

Linnik was born in Bila Tserkva, in present-day Ukraine. He went to Saint Petersburg University where his supervisor was Vladimir Tartakovsky, and later worked at that university and the Steklov Institute. He was a member of the Academy of Sciences of the Soviet Union, as was his father, Vladimir Pavlovich Linnik. He was awarded both Stalin and Lenin Prizes. He died in Leningrad.[1]

Work in number theory

[edit]

Work in probability theory and statistics

[edit]

Infinitely divisible distributions

[edit]

Linnik obtained numerous results concerning infinitely divisible distributions.[4] In particular, he proved the following generalisation of Cramér's theorem: any divisor of a convolution of Gaussian and Poisson random variables is also a convolution of Gaussian and Poisson.

He has also coauthored the book Linnik & Ostrovskii (1977) on the arithmetics of infinitely divisible distributions.

Central limit theorem

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Statistics

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Selected publications

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  • Linnik, Yu.V. (1971), Independent and stationary sequences of random variables, Series of Monographs and Textbooks on Pure and Applied Mathematics, Groningen: Wolters-Noordhoff Publishing
  • Linnik, Yu.V. (1961), Method of least squares and principles of the theory of observations, New York-Oxford-London-Paris: Pergamon Press, MR 0124121
  • Linnik, Yu.V.; Ostrovskii, I.V. (1977), Decomposition of random variables and vectors, Translations of Mathematical Monographs, vol. 48, Providence, R.I.: American Mathematical Society
  • Linnik, Yu.V. (1968), Ergodic properties of algebraic fields, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 45, New York: Springer-Verlag New York Inc.

Notes

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  1. ^ Faddeyev, D. K.; Lozinsky, S. M.; Malyshev, A. V. (1975), "Yuri V. Linnik (1915–1972): a biographical note", Acta Arith., 27: 1–2, doi:10.4064/aa-27-1-1-2, MR 0421941.
  2. ^ Bredikhin, B.M. (2001) [1994], "Density method", Encyclopedia of Mathematics, EMS Press
  3. ^ Michel, Ph.; Venkatesh, A. (2006), "Equidistribution, L-functions and ergodic theory: on some problems of Yu. V. Linnik", Proceedings of ICM 2006, vol. 2, Zurich: Eur. Math. Soc., pp. 421–457
  4. ^ Ibragimov, I. A. (1992), "Yu. V. Linnik. Some of his work from the 1950s", St. Petersburg Math. J., 3 (3): 687–696, MR 1150561.
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