Aleksandr Ya. Khinchin

Aleksandr Yakovlevich Khinchin (Russian Александр Яковлевич Хинчин) (July 19, 1894 – November 18, 1959) was a Russian mathematician and one of the most significant people in the Soviet school of probability theory. He was born in the village of Kondrovo, Kaluga Governorate, Russia. 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. Image File history File links Khinchin. ... Image File history File links Khinchin. ... July 19 is the 200th day (201st in leap years) of the year in the Gregorian Calendar, with 165 days remaining. ... 1894 (MDCCCXCIV) was a common year starting on Monday (see link for calendar). ... November 18 is the 322nd day of the year (323rd in leap years) in the Gregorian Calendar. ... Year 1959 (MCMLIX) was a common year starting on Thursday of the Gregorian calendar. ... Leonhard Euler is considered by many to be one of the greatest mathematicians of all time A mathematician is the person whose primary area of study and research is the field of mathematics. ... Motto: Пролетарии всех стран, соединяйтесь! (Transliterated: Proletarii vsekh stran, soedinyaytes!) Translation: Workers of the world, unite!) Anthem: The Internationale (1922-1944) Hymn of the Soviet Union (1944-1991) Capital (and largest city) Moscow Official languages None; Russian de facto Government Socialist Republic/Federation of Soviet Republics  - Last President Mikhail Gorbachev  - Last Premier Ivan Silayev... Probability theory is the mathematical study of phenomena characterized by randomness or uncertainty. ... Kaluga Oblast (Russian: ) (29,900 km², pop. ... Moscow State University M.V. Lomonosov Moscow State University (Russian: Московский государственный университет имени Ðœ.Ð’.Ломоносова, often abbreviated МГУ, MSU, MGU) is the largest and the oldest university in Russia, founded in 1755. ... Nikolai Nikolaevich Luzin (Никола́й Никола́евич Лу́зин) (December 9, 1883 - January 28, 1950), Soviet/Russian mathematician. ... Year 1916 (MCMXVI) was a leap year starting on Saturday (link will display the full calendar). ...

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 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 the property now known as Khinchin's constant. He also published several important works on statistical physics, where he used the methods of probability theory, and on information theory, queuing theory and mathematical analysis. Real analysis is a branch of mathematical analysis dealing with the set of real numbers and functions of real numbers. ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... In probability theory, the law of the iterated logarithm is the name given to several theorems which describe the magnitude of the fluctuations of a random walk. ... Year 1924 (MCMXXIV) was a leap year starting on Tuesday (link will display the full calendar). ... In economics, Edgeworths limit theorem examines the range of possible outcomes which may result from free market exchange or barter between groups of people. ... In the mathematical sciences, a stationary process (or strict(ly) stationary process) is a stochastic process in which the probability density function of some random variable X does not change over time or position. ... In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers. ... In mathematics, a continued fraction is an expression such as where a0 is some integer and all the other numbers an are positive integers. ... In number theory, Aleksandr Yakovlevich Khinchin proved that for almost all real numbers x, the infinitely many terms ai of the continued fraction expansion of x have an astonishing property: their geometric mean is a constant, known as Khinchins constant, which is independent of the value of x. ... Statistical physics, one of the fundamental theories of physics, uses methods of statistics in solving physical problems. ... A bundle of optical fiber. ... Queueing theory (spelled queuing theory in the United States) is the mathematical study of waiting lines (or queues). ... Analysis is the branch of mathematics most explicitly concerned with the notion of a limit, either the limit of a sequence or the limit of a function. ...

In 1939 Khinchin was elected as a Correspondent Member of the Academy of Sciences of the USSR. He was awarded the USSR State Prize (1941), the Order of Lenin, three other orders, and medals. 1939 (MCMXXXIX) was a common year starting on Sunday (link will take you to calendar). ... Russian Academy of Sciences (Росси́йская Акаде́мия Нау́к) is the national academy of Russia. ... Stalin Prize medal State Prize medal The USSR State Prize (Russian:Госуда́рственная пре́мия СССР) was the Soviet Unions highest civilian honour. ... The Order of Lenin (ru: Орден Ленина), named after the leader of the Russian Revolution, was the second highest national order of the Soviet Union (Highest was the Order of Victory). ...

He died in Moscow, USSR. Location Position of Moscow in Europe Government Country District Subdivision Russia Central Federal District Federal City Mayor Yuriy Luzhkov Geographical characteristics Area  - City 1,081 km² Population  - City (2007)    - Density 10,469,000   8537. ...

See also

• Khinchin's theorem
• Wiener–Khinchin theorem
• Khinchin's constant
• Khinchin–Lévy constant
• Equidistribution theorem
• Continued fraction

The Wiener–Khinchin theorem (also known as the Wiener–Khintchine theorem and sometimes as the Khinchin–Kolmogorov theorem) states that the power spectral density of a wide-sense-stationary random process is the Fourier Transform of the corresponding autocorrelation function. ... In number theory, Aleksandr Yakovlevich Khinchin proved that for almost all real numbers x, the infinitely many terms ai of the continued fraction expansion of x have an astonishing property: their geometric mean is a constant, known as Khinchins constant, which is independent of the value of x. ... In mathematics Lévys constant (sometimes known as the Khinchin–Lévy constant) occurs in an expression for the asymptotic behaviour of the denominators of the convergents of continued fractions. ... In mathematics, the equidistribution theorem is the statement that the sequence a, 2a, 3a, ... mod 1 is uniformly distributed on the unit interval, when a is an irrational number. ... In mathematics, a continued fraction is an expression such as where a0 is some integer and all the other numbers an are positive integers. ...

Bibliography

• Sur la Loi des Grandes Nombres, in Comptes Rendus de l'Academie des Sciences, Paris, 1929
• Continued Fractions, Mineola, N.Y. : Dover Publications, 1997, ISBN 0-486-69630-8 (first published in Moscow, 1935)
• Three Pearls of Number Theory, Mineola, NY : Dover Publications, 1998, ISBN 0-486-40026-3 (first published in Moscow and Leningrad, 1947)
• Mathematical Foundations of Quantum Statistics, Mineola, N.Y. : Dover Publications, 1998, ISBN 0-486-40025-5 (first published in Moscow and Leningrad, 1951)

Location Position of Moscow in Europe Government Country District Subdivision Russia Central Federal District Federal City Mayor Yuriy Luzhkov Geographical characteristics Area  - City 1,081 km² Population  - City (2007)    - Density 10,469,000   8537. ... Saint Petersburg (Russian: Санкт-Петербу́рг, English transliteration: Sankt-Peterburg), colloquially known as Питер (transliterated Piter), formerly known as Leningrad (Ленингра́д, 1924–1991) and... Location Position of Moscow in Europe Government Country District Subdivision Russia Central Federal District Federal City Mayor Yuriy Luzhkov Geographical characteristics Area  - City 1,081 km² Population  - City (2007)    - Density 10,469,000   8537. ... Saint Petersburg (Russian: Санкт-Петербу́рг, English transliteration: Sankt-Peterburg), colloquially known as Питер (transliterated Piter), formerly known as Leningrad (Ленингра́д, 1924–1991) and...

External links

• Aleksandr Khinchin at the Mathematics Genealogy Project
• O'Connor, John J., and Edmund F. Robertson. "Aleksandr Khinchin". MacTutor History of Mathematics archive.