Yuri Linnik

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Yuri V. Linnik

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.

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. He was a member of the Russian Academy of Sciences, as was his father, Vladimir Pavlovich Linnik. He was awarded both State 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[edit]

Statistics[edit]

Selected publications[edit]

  • 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 48, Providence, R.I.: American Mathematical Society 
  • Linnik, Yu.V. (1968), Ergodic properties of algebraic fields, Ergebnisse der Mathematik und ihrer Grenzgebiete 45, New York: Springer-Verlag New York Inc. 

Notes[edit]

  1. ^ Faddeyev, D. K.; Lozinsky, S. M.; Malyshev, A. V. (1975), Yuri V. Linnik (1915–1972): a biographical note, Acta Arith. 27: 1–2, MR 0421941. 
  2. ^ Bredikhin, B.M. (2001), "Density method", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4 
  3. ^ Michel, Ph.; Venkatesh, A. (2006), "Equidistribution, L-functions and ergodic theory: on some problems of Yu. V. Linnik", Proceedings of ICM 2006 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. 

External links[edit]