Aleksandr Yakovlevich Khinchin
Encyclopedia
Aleksandr Yakovlevich Khinchin was a Soviet 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
, 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 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 approximation
s and established an important result for simple real continued fraction
s, discovering a property of such numbers that leads to what is 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
.
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.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and one of the most significant people in the Soviet
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
school of probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
. He was born in the village of Kondrovo
Kondrovo
Kondrovo is a town and the administrative center of Dzerzhinsky District of Kaluga Oblast, Russia, located on the Shanya River , northwest of Kaluga...
, Kaluga Governorate
Kaluga Oblast
Kaluga Oblast is a federal subject of Russia . Its administrative center is the city of Kaluga.-Geography:Kaluga Oblast is located in the central part of the East European Plain. The Smolensk Highland lays in the western and north-western part of the oblast, while the Central Russian Highland -...
, Russian Empire
Russian Empire
The Russian Empire was a state that existed from 1721 until the Russian Revolution of 1917. It was the successor to the Tsardom of Russia and the predecessor of the Soviet Union...
. While studying at Moscow State University
Moscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
, he became one of the first followers of the famous Luzin
Nikolai Luzin
Nikolai Nikolaevich Luzin, , was a Soviet/Russian mathematician known for his work in descriptive set theory and aspects of mathematical analysis with strong connections to point-set topology. He was the eponym of Luzitania, a loose group of young Moscow mathematicians of the first half of the...
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
Real analysis
Real analysis, is a branch of mathematical analysis dealing with the set of real numbers and functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real...
. Later he applied methods from the metric theory of functions to problems in probability theory and number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
. He became one of the founders of modern probability theory, discovering the law of the iterated logarithm
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. Y. Khinchin . Another statement was given by A.N...
in 1924, achieving important results in the field of limit theorems
Central limit theorem
In probability theory, the central limit theorem states conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed. The central limit theorem has a number of variants. In its common...
, giving a definition of a stationary process
Stationary process
In the mathematical sciences, a stationary process is a stochastic process whose joint probability distribution does not change when shifted in time or space...
and laying a foundation for the theory of such processes. Khinchin made significant contributions to the metric theory of Diophantine approximation
Diophantine approximation
In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers....
s and established an important result for simple real continued fraction
Continued fraction
In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on...
s, discovering a property of such numbers that leads to what is now known as Khinchin's constant. He also published several important works on statistical physics
Statistical physics
Statistical physics is the branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic...
, where he used the methods of probability theory, and on information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
, queuing theory and mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
.
In 1939 Khinchin was elected as a Correspondent Member of the Academy of Sciences of the USSR. He was awarded the Stalin Prize
USSR State Prize
The USSR State Prize was the Soviet Union's state honour. It was established on September 9, 1966. After the breakup of the Soviet Union, the prize was followed up by the State Prize of the Russian Federation....
(1941), the Order of Lenin
Order of Lenin
The Order of Lenin , named after the leader of the Russian October Revolution, was the highest decoration bestowed by the Soviet Union...
, three other orders, and medals.
See also
- Pollaczek–Khinchine formula
- Wiener–Khinchin theoremWiener–Khinchin theoremThe Wiener–Khinchin theorem states that the power spectral density of a wide–sense stationary random process is the Fourier transform of the corresponding autocorrelation function.-History:Norbert Wiener first published the result in...
- Khinchin inequality
- Equidistribution theoremEquidistribution theoremIn mathematics, the equidistribution theorem is the statement that the sequenceis uniformly distributed on the unit interval, when a is an irrational number...
- Khinchin–Lévy constant