Aleksandr Yakovlevich Khinchin (russian: Алекса́ндр Я́ковлевич Хи́нчин, french: Alexandre Khintchine; July 19, 1894 – November 18, 1959) was a
Soviet mathematician and one of the most significant contributors to the Soviet school of
probability theory.
Life and career
He was born in the village of
Kondrovo,
Kaluga Governorate,
Russian Empire. While studying at
Moscow State University, he became one of the first followers of the famous
Luzin school. Khinchin graduated from the university in 1916 and six years later he became a full professor there, retaining that position until his death.
Khinchin's early works focused on
real analysis. Later he applied methods from the metric theory of functions to problems in probability theory and
number theory. He became one of the founders of modern probability theory, discovering the
law of the iterated logarithm
In probability theory, the law of the iterated logarithm describes the magnitude of the fluctuations of a random walk. The original statement of the law of the iterated logarithm is due to A. Ya. Khinchin (1924). Another statement was given by A ...
in 1924, achieving important results in the field of
limit theorems, giving a definition of a
stationary process and laying a foundation for the theory of such processes.
Khinchin made significant contributions to the metric theory of
Diophantine approximations and established an important result for simple real
continued fractions, discovering a property of such numbers that leads to what is now known as
Khinchin's constant In number theory, Aleksandr Yakovlevich Khinchin proved that for almost all real numbers ''x'', coefficients ''a'i'' of the continued fraction expansion of ''x'' have a finite geometric mean that is independent of the value of ''x'' and is kno ...
. He also published several important works on
statistical physics, where he used the methods of probability theory, and on
information theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...
,
queuing theory and
mathematical analysis.
In 1939 Khinchin was elected as a Correspondent Member of the
Academy of Sciences of the USSR. He was awarded the
Stalin Prize (1941), the
Order of Lenin, three other orders, and medals.
See also
*
Pollaczek–Khinchine formula In queueing theory, a discipline within the mathematical theory of probability, the Pollaczek–Khinchine formula states a relationship between the queue length and service time distribution Laplace transforms for an M/G/1 queue (where jobs arri ...
*
Wiener–Khinchin theorem
*
Khinchin inequality In mathematics, the Khintchine inequality, named after Aleksandr Khinchin and spelled in multiple ways in the Latin alphabet, is a theorem from probability, and is also frequently used in mathematical analysis, analysis. Heuristically, it says that ...
*
Equidistribution theorem
*
Khinchin's constant In number theory, Aleksandr Yakovlevich Khinchin proved that for almost all real numbers ''x'', coefficients ''a'i'' of the continued fraction expansion of ''x'' have a finite geometric mean that is independent of the value of ''x'' and is kno ...
*
Khinchin–Lévy constant
*
Khinchin's theorem on Diophantine approximations
In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria.
The first problem was to know how well a real number can be approximated by r ...
*
Law of the iterated logarithm
In probability theory, the law of the iterated logarithm describes the magnitude of the fluctuations of a random walk. The original statement of the law of the iterated logarithm is due to A. Ya. Khinchin (1924). Another statement was given by A ...
*
Palm-Khintchine Theorem
*
Weak law of large numbers (Khinchin's law)
*Lévy–Khintchin formula of characteristic function of
Lévy process
Bibliography
*''Sur la Loi des Grandes Nombres'', in ''Comptes Rendus de l'Académie des Sciences'', Paris, 1929
*''Asymptotische Gesetze der Wahrscheinlichkeitsrechnung'', Berlin: Julius Springer, 1933
*''Continued Fractions'', Mineola, N.Y. : Dover Publications, 1997, (first published in Moscow, 1935)
*''Three Pearls of Number Theory'', Mineola, NY : Dover Publications, 1998, (first published in
Moscow and
Leningrad, 1947)
*''Mathematical Foundations of Quantum Statistics'', Mineola, N.Y. : Dover Publications, 1998, (first published in Moscow and Leningrad, 1951; trans. in 1960 by Irwin Shapiro)
*''Mathematical Foundations of Information Theory'', Dover Publications, 1957,
References
External links
*
*
List of books by Khinchin provided by National Library of AustraliaA.Ya. Khinchin
a
Math-Net.Ru
{{DEFAULTSORT:Khinchin, Aleksandr Yakovlevich
20th-century Russian mathematicians
Soviet mathematicians
Number theorists
Probability theorists
Queueing theorists
Stalin Prize winners
Moscow State University alumni
Moscow State University faculty
Corresponding Members of the USSR Academy of Sciences
1894 births
1959 deaths
Burials at Donskoye Cemetery