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Paul Lévy (mathematician)

April 16, 2024

For other uses, see Paul Lévy (disambiguation).

Paul Pierre Lévy (15 September 1886 – 15 December 1971)[2] 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.

Paul Lévy
Paul Pierre Lévy
Born(1886-09-15)15 September 1886
Paris, France
Died15 December 1971(1971-12-15) (aged 85)
Paris, France
NationalityFrench
Alma materUniversity of Paris
Known forAdditive process
Brownian excursion
Concentration of measure
Martingale (probability theory)
Universal chord theorem
Lévy alpha-stable distribution
Lévy's arcsine law
Lévy C curve
Lévy's constant
Lévy characterisation
Lévy's continuity theorem
Lévy distribution
Lévy flight
Lévy's local time
Lévy measure
Lévy's modulus of continuity theorem
Lévy process
Lévy's zero–one law
Lévy–Khintchine representation
Lévy–Prokhorov metric
Lévy–Steinitz theorem
Lindeberg–Lévy CLT
Wiener–Lévy theorem
AwardsEmile Picard Medal of the French Academy of Sciences (1953)[1]
Scientific career
FieldsMathematics
InstitutionsÉcole Polytechnique
École des Mines
Doctoral advisorJacques Hadamard
Vito Volterra
Doctoral studentsWolfgang Doeblin
Michel Loève
Benoît Mandelbrot
Georges Matheron

Biography edit

Lévy was born in Paris to a Jewish family which already included several mathematicians.[3] 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.[2]

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.[2]

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 Aleksandr Khinchin, 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.[4]

Works edit

  • 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 edit

References edit

  1. ^ Médaille Emile Picard
  2. ^ a b c O'Connor, John J.; Robertson, Edmund F., "Paul Lévy (mathematician)", MacTutor History of Mathematics Archive, University of St Andrews
  3. ^ Barbut, Marc; Locker, Bernard; Mazliak, Laurent (2013). Paul Lévy and Maurice Fréchet: 50 Years of Correspondence in 107 Letters. p. xii. ISBN 978-1-4471-5618-5.
  4. ^ Kosmann-Schwarzbach, Yvette (2015), "Women mathematicians in France in the mid-twentieth century", BSHM Bulletin: Journal of the British Society for the History of Mathematics, 30 (3): 227–242, arXiv:1502.07597, doi:10.1080/17498430.2014.976804, S2CID 119148294.

External links edit

April 16, 2024
paul, lévy, mathematician, other, uses, paul, lévy, disambiguation, paul, pierre, lévy, september, 1886, december, 1971, french, mathematician, active, especially, probability, theory, introducing, fundamental, concepts, such, local, time, stable, distribution. For other uses see Paul Levy disambiguation Paul Pierre Levy 15 September 1886 15 December 1971 2 was a French mathematician who was active especially in probability theory introducing fundamental concepts such as local time stable distributions and characteristic functions Levy processes Levy flights Levy measures Levy s constant the Levy distribution the Levy area the Levy arcsine law and the fractal Levy C curve are named after him Paul LevyPaul Pierre LevyBorn 1886 09 15 15 September 1886Paris FranceDied15 December 1971 1971 12 15 aged 85 Paris FranceNationalityFrenchAlma materUniversity of ParisKnown forAdditive processBrownian excursionConcentration of measureMartingale probability theory Universal chord theoremLevy alpha stable distributionLevy s arcsine lawLevy C curveLevy s constantLevy characterisationLevy s continuity theoremLevy distributionLevy flightLevy s local timeLevy measureLevy s modulus of continuity theoremLevy processLevy s zero one lawLevy Khintchine representationLevy Prokhorov metricLevy Steinitz theoremLindeberg Levy CLTWiener Levy theoremAwardsEmile Picard Medal of the French Academy of Sciences 1953 1 Scientific careerFieldsMathematicsInstitutionsEcole PolytechniqueEcole des MinesDoctoral advisorJacques HadamardVito VolterraDoctoral studentsWolfgang DoeblinMichel LoeveBenoit MandelbrotGeorges Matheron Contents 1 Biography 2 Works 3 See also 4 References 5 External linksBiography editLevy was born in Paris to a Jewish family which already included several mathematicians 3 His father Lucien Levy was an examiner at the Ecole Polytechnique Levy attended the Ecole Polytechnique and published his first paper in 1905 at the age of nineteen while still an undergraduate in which he introduced the Levy 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 Ecole des Mines where he became a professor in 1913 2 During World War I Levy conducted mathematical analysis work for the French Artillery In 1920 he was appointed Professor of Analysis at the Ecole Polytechnique where his students included Benoit Mandelbrot and Georges Matheron He remained at the Ecole Polytechnique until his retirement in 1959 with a gap during World War II after his 1940 firing because of the Vichy anti Jewish legislation 2 Levy 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 Theorie de l addition des variables aleatoires using the notion of characteristic function He also introduced independently from Aleksandr Khinchin the notion of infinitely divisible law and derived their characterization through the Levy Khintchine representation His 1948 monograph on Brownian motion Processus stochastiques et mouvement brownien contains a wealth of new concepts and results including the Levy area the Levy arcsine law the local time of a Brownian path and many other results Levy received a number of honours including membership at the French Academy of Sciences and honorary membership at the London Mathematical Society His daughter Marie Helene Schwartz and son in law Laurent Schwartz were also notable mathematicians 4 Works edit1922 Lecons d analyse Fonctionnelle 1925 Calcul des probabilites 1937 Theorie de l addition des variables aleatoires 1948 Processus stochastiques et mouvement brownien 1954 Le mouvement brownienSee also editCramer s decomposition theorem Levy distribution Levy metric Levy s modulus of continuity Levy Prokhorov metric Levy s continuity theorem Levy s zero one law Concentration of measure Levy process Levy Khintchine representation Levy Ito decomposition Levy flight local time Isoperimetric inequality on a sphere Levy s characterisation of Brownian motionReferences edit Medaille Emile Picard a b c O Connor John J Robertson Edmund F Paul Levy mathematician MacTutor History of Mathematics Archive University of St Andrews Barbut Marc Locker Bernard Mazliak Laurent 2013 Paul Levy and Maurice Frechet 50 Years of Correspondence in 107 Letters p xii ISBN 978 1 4471 5618 5 Kosmann Schwarzbach Yvette 2015 Women mathematicians in France in the mid twentieth century BSHM Bulletin Journal of the British Society for the History of Mathematics 30 3 227 242 arXiv 1502 07597 doi 10 1080 17498430 2014 976804 S2CID 119148294 External links editRama Cont Paul Levy a biography Gerard P Michon Paul Levy and Functional Analysis Paul Levy at the Mathematics Genealogy Project O Connor John J Robertson Edmund F Paul Levy mathematician MacTutor History of Mathematics Archive University of St Andrews Retrieved from https en wikipedia org w index php title Paul Levy mathematician amp oldid 1214397719, wikipedia, wiki, book, books, library,

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