Aleksandr Ya. Khinchin

Aleksandr Yakovlevich Khinchin (Russian Александр Яковлевич Хинчин) (July 19, 1894 – November 18, 1959) was a Russian mathematician, who was one of the most significant people in the Soviet school of probability theory. He was born in village Kondrovo, Kaluga Governorate, Russia. Studying at Moscow State University, he became one of the first followers of the famous Luzin's school. In 1916 Khinchin graduated from the university and six years later became a full professor there, keeping 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 with 43 days remaining. ... 1959 (MCMLIX) was a common year starting on Thursday of the Gregorian calendar. ... Leonhard Euler is considered by many people to be one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is mathematics. ... State motto (Russian): Пролетарии всех стран, соединяйтесь! (Transliterated: Proletarii vsekh stran, soedinyaytes!) (Translated: Workers of the world, unite!) Capital Moscow Official language None; Russian (de facto) Government Federation of Soviet republics Area  - Total  - % water 1st before collapse 22,402,200 km² Approx. ... Probability theory is the mathematical study of probability. ... 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 arguably the oldest university in Russia, founded in 1755. ... Nikolai Nikolaevich Luzin (Никола́й Никола́евич Лу́зин) (December 9, 1883 - January 28, 1950), Soviet/Russian mathematician. ... 1916 (MCMXVI) was a leap year starting on Saturday (link will take you to calendar). ...

Khinchin's early works focused on real analysis. Later he used methods of the metric theory of functions in probability theory and number theory. He became one of the founders of the modern probability theory, discovering 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. In number theory Khinchin made significant contributions to the metric theory of Diophantine approximations and established an important result for real continued fractions, discovering their property, known as Khinchin's constant. He also published several important works on statistical physics, where he used methods of probability theory, on information theory, queuing theory and mathematical analysis. Real analysis is that branch of mathematical analysis dealing with the set of real numbers and functions of real numbers. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... 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. ... 1924 (MCMXXIV) was a leap year starting on Tuesday (link will take you to 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. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Queueing theory (spelled queuing theory in the United States) is the mathematical study of waiting lines (or queues). ... Analysis is the generic name given to any branch of mathematics that depends upon the concepts of limits and convergence. ...

In 1939 Khinchin was elected as a Correspondent Member of the Academy of Sciences of USSR. He was awarded the USSR State Prize (1941), 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. For other uses, see Moscow (disambiguation). ...

See also

• Khinchin's theorem
• Wiener–Khinchin theorem
• 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 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 0486696308 (first published in Moscow, 1935)
• Three Pearls of Number Theory, Mineola, NY : Dover Publications, 1998, ISBN 0486400263 (first published in Moscow and Leningrad, 1947)
• Mathematical Foundations of Quantum Statistics, Mineola, N.Y. : Dover Publications, 1998, ISBN 0486400255 (first published in Moscow and Leningrad, 1951)

For other uses, see Moscow (disambiguation). ... Saint Petersburg (Russian: Санкт-Петербу́рг, English transliteration: Sankt-Peterburg), colloquially known as Питер (transliterated Piter), formerly known as Leningrad (Ленингра́д, 1924–1991) and Petrograd (Петрогра́д, 1914–1924), is a city located in Northwestern Russia on the delta of the river Neva at the east end of the Gulf of Finland... For other uses, see Moscow (disambiguation). ... Saint Petersburg (Russian: Санкт-Петербу́рг, English transliteration: Sankt-Peterburg), colloquially known as Питер (transliterated Piter), formerly known as Leningrad (Ленингра́д, 1924–1991) and Petrograd (Петрогра́д, 1914–1924), is a city located in Northwestern Russia on the delta of the river Neva at the east end of the Gulf of Finland...

External links

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