Paul Lévy (mathematician)

Paul Lévy (mathematician)
Paul Pierre Lévy (15 September 1886 – 15 December 1971) was a French mathematician who was active especially in probability theory, introducing fundamental concepts such as local time, stable distributions and characteristic functions. Lévy processes, Lévy flights, Lévy measures, Lévy's constant, the Lévy distribution, the Lévy area, the Lévy arcsine law, and the fractal Lévy C curve are named after him.
Biography
Lévy was born in Paris to a Jewish family which already included several mathematicians. His father Lucien Lévy was an examiner at the École Polytechnique. 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. His teacher and advisor was Jacques Hadamard. 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 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 and Georges Matheron. 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, Processus stochastiques et mouvement brownien, contains a wealth of new concepts and results, including the Lévy area, the Lévy arcsine law,
the local time 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
See also
Cramér's decomposition theorem
Lévy distribution
Lévy metric
Lévy's modulus of continuity
Lévy–Prokhorov metric
Lévy's continuity theorem
Lévy's zero-one law
Concentration of measure
Lévy process
Lévy–Khintchine representation
Lévy–Itô decomposition
Lévy flight
local time
Isoperimetric inequality on a sphere
Lévy's characterisation of Brownian motion
References
External links
Rama Cont: Paul Lévy: a biography
Gérard P. Michon: Paul Lévy and Functional Analysis
Jewish French scientists
École Polytechnique alumni
Mines Paris - PSL 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
University of Paris alumni