Paul Pierre Lévy (15 September 1886 – 15 December 1971) was a French mathematician who was active especially in

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...

, introducing fundamental concepts such as

local time Local time is the time observed in a specific locality. There is no canonical definition. Originally it was mean solar time, but since the introduction of time zones it is generally the time as determined by the time zone in effect, with daylight s ...

stable distributions In probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be sta ...

and characteristic functions.

Lévy process In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments: it represents the motion of a point whose successive displacements are random, in which disp ...

es, Lévy flights,

Lévy measure Levy, Lévy or Levies may refer to: People * Levy (surname), people with the surname Levy or Lévy * Levy Adcock (born 1988), American football player * Levy Barent Cohen (1747–1808), Dutch-born British financier and community worker * Levy ...

s, Lévy's constant, the

Lévy distribution In probability theory and statistics, the Lévy distribution, named after Paul Lévy, is a continuous probability distribution for a non-negative random variable. In spectroscopy, this distribution, with frequency as the dependent variable, is k ...

, the Lévy area, the Lévy arcsine law, and the fractal

Lévy C curve In mathematics, the Lévy C curve is a self-similar fractal curve that was first described and whose differentiability properties were analysed by Ernesto Cesàro in 1906 and Georg Faber in 1910, but now bears the name of French mathematician Pa ...

are named after him.

Biography

Lévy was born in

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), ma ...

to a

Jew Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""T ...

ish family which already included several mathematicians. His father Lucien Lévy was an examiner at the

École Polytechnique École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

. Lévy attended the École Polytechnique and published his first paper in 1905, at the age of nineteen, while still an undergraduate, in which he introduced the

Lévy–Steinitz theorem In mathematics, the Lévy–Steinitz theorem identifies the set of values to which rearrangements of an infinite series of vectors in R''n'' can converge. It was proved by Paul Lévy in his first published paper when he was 19 years old. In 1913 Er ...

. His teacher and advisor was

Jacques Hadamard Jacques Salomon Hadamard (; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex analysis, differential geometry and partial differential equations. Biography The son of a teac ...

. After graduation, he spent a year in military service and then studied for three years at the École des Mines, where he became a professor in 1913. During

World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...

Lévy conducted mathematical analysis work for the French Artillery. In 1920 he was appointed Professor of Analysis at the École Polytechnique, where his students included

Benoît Mandelbrot Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of phy ...

and

Georges Matheron Georges François Paul Marie Matheron (2 December 1930 – 7 August 2000) was a French mathematician and civil engineer of mines, known as the founder of geostatistics and a co-founder (together with Jean Serra) of mathematical morphology. In 196 ...

. He remained at the École Polytechnique until his retirement in 1959, with a gap during World War II after his 1940 firing because of the Vichy anti-Jewish legislation. Lévy made many fundamental contributions to probability theory and the nascent theory of stochastic processes. He introduced the notion of 'stable distribution' which share the property of stability under addition of independent variables and proved a general version of the Central Limit theorem, recorded in his 1937 book ''Théorie de l'addition des variables aléatoires'', using the notion of characteristic function. He also introduced, independently from Ya. Khinchine, the notion of infinitely divisible law and derived their characterization through the Lévy–Khintchine representation. His 1948 monograph on

Brownian motion Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of random fluctuations in a particle's position insi ...

, ''Processus stochastiques et mouvement brownien'', contains a wealth of new concepts and results, including the Lévy area, the Lévy arcsine law, the

of a Brownian path, and many other results. Lévy received a number of honours, including membership at the French Academy of Sciences and honorary membership at the London Mathematical Society. His daughter Marie-Hélène Schwartz and son-in-law Laurent Schwartz were also notable mathematicians..

Works

* 1922 – ''Lecons d'analyse Fonctionnelle'' * 1925 – ''Calcul des probabilités'' * 1937 – ''Théorie de l'addition des variables aléatoires'' * 1948 – ''Processus stochastiques et mouvement brownien'' * 1954 – ''Le mouvement brownien''

References

External links

* Rama Cont:
Paul Lévy: a biography
* Gérard P. Michon:

* * {{DEFAULTSORT:Levy, Paul Pierre Jewish French scientists École Polytechnique alumni Mines ParisTech alumni Corps des mines 1886 births 1971 deaths 20th-century French mathematicians 19th-century French Jews Probability theorists Members of the French Academy of Sciences

Biography

Works

See also

References

External links