mathematics

Jacques Neveu

Jacques Neveu is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Jacques Neveu rather than just read about it. In short: Jacques Jean-Pierre Neveu (14 November 1932 – 17 May 2016) was a Belgian (and then French) mathematician, specializing in probability theory. He is one of the founders of the French school (post WW II) of probability and statistics.

Key takeaways

Jacques Neveu belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Jacques Neveu to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Jacques Neveu from memory before moving on to harder problems.

Reference excerpt

Jacques Jean-Pierre Neveu (14 November 1932 – 17 May 2016) was a Belgian (and then French) mathematician, specializing in probability theory. He is one of the founders of the French school (post WW II) of probability and statistics.

Education and career Jacques Neveu received in 1955 from the Sorbonne his doctorate in mathematics under Robert Fortet with dissertation Étude des semi-groupes de Markov. In 1960, Neveu was, with Robert Fortet, one of the first two members of the Laboratoire de Probabilités et Modèles Aléatoires (LPMA). He was the LPMA's director from 1980 until 1989 when Jean Jacod became the director. In 1962, Neveu was a chargé de cours (university lecturer) at the Collège de France. He taught at the Sorbonne and, after the reorganization of the University of Paris, at the University of Paris VI at the Laboratory for Probability of the Institut de mathématiques de Jussieu. He was a professor at the École Polytechnique. In 1976, he gave a course at l'école d'été de Saint-Flour (a summer school in probability theory sponsored by the University of Clermont Auvergne). He was a visiting professor in Brussels, São Paulo, and Leuven. From 1969 to 1987, Neveu was the thesis advisor for 19 doctoral students. In 1977, he was the president of the Société mathématique de France. In 1991, he founded the group Modélisation Aléatoire et Statistique (MAS) of the Société de Mathématiques Appliquées et Industrielles (SMAI). In 2012, he was elected a Fellow of the American Mathematical Society.

Research Neveu is one of the founders of the modern theory of probability. His research deals with Markov processes, Markov chains, Gaussian processes, martingales, ergodic theory, random trees (especially Galton-Watson processes and Galton-Watson trees), and Dirac measures, as well as applications of probability theory to statistics, computer science, combinatorics, and statistical physics. In 1986 he introduced the concept of arbre de Galton-Watson (Galton-Watson tree) within the framework of discrete random trees; within the mathematical formalism of Galton-Watson trees, the notation de Neveu is named in his honor.

Commemoration Several mathematicians have paid tribute to Neveu for his influence on the modern theory of probability. He was outstanding in teaching as well as research. In honor of Neveu, a prize is awarded by the MAS group of the SMAI to the year's best of the new French holders of doctorates in mathematicians or statistics on the basis of the judged quality of the dissertation.

Prix Jacques Neveu The laureates are:

2008: Pierre Nolin; 2009: Amandine Véber; 2010: Sébastien Bubeck & Kilian Raschel; 2011: Nicolas Curien; 2012: Pierre Jacob et Quentin Berger; 2013: Adrien Kassel; 2014: Emilie Kaufmann & Julien Reygner; 2015: Erwin Scornet; 2016: Anna Ben-Hamou; 2017: Aran Raoufi; 2018: Elsa Cazelles.

Selected publications

Articles "Lattice methods and submarkovian processes." In Fourth Berkeley Symposium on Mathematical Statistics and Probability, pp. 347–391. 1961. "Existence of bounded invariant measures in ergodic theory." In Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), vol. 2, no. Part 2, pp. 461–472. 1967. "Temps d'arrêt d'un système dynamique." Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 13, no. 2, 1969, pp. 81–94. doi:10.1007/BF00537013 "Potentiel Markovien récurrent des chaînes de Harris." Ann. Inst. Fourier, vol. 22, no. 2, 1972, pp. 85–130. "Sur l’espérance conditionelle par rapport à un mouvement brownien." Ann. Inst. H. Poincaré, section B, vol. 12, no. 2, 1976, pp. 105–109. "Processus ponctuels." In École d’Eté de Probabilités de Saint-Flour VI-1976, pp. 249–445. Springer, Berlin, Heidelberg, 1977. doi:10.1007/BFb0097494 Arbres et processus de Galton-Watson, Annales de l'IHP, section B, vol. 22, 1986, pp. 199–207. "Multiplicative martingales for spatial branching processes." In Seminar on Stochastic Processes, 1987, pp. 223–242. Birkhäuser Boston, 1988. doi:10.1007/978-1-4684-0550-7_10 with Francis Comets: The Sherrington-Kirkpatrick model of spin glasses and stochastic calculus: the high temperature case. Communications in Mathematical Physics, vol. 166, no. 3, 1995, pp. 549–564. doi:10.1007/BF02099887

Books Théorie des semi-groups de Markov, University of California Press 1958 (and Gauthier-Villars 1958) Bases mathématiques du calcul des probabilités, Masson, 1964, 1970 English translation: Mathematical foundations of the calculus of probability, Holden-Day 1965 Processus aléatoires gaulliens, Montréal: Presses de l'Université de Montréal, 1968 Cours de probabilités, École Polytechnique, 1970, 1978 Martingales à temps discret, Masson, 1972 English translation: Discrete-parameter martingales, Elsevier, 1975 Théorie de la mesure et intégration, cours de l'École polytechnique, 1983 Introduction aux processus aléatoires, École Polytechnique 1985

References

Illustrations

Worked examples

Example 1 — a first encounter with Jacques Neveu

Start with the simplest possible case. Write down what Jacques Neveu claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Jacques Neveu before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Jacques Neveu ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Jacques Neveu

In research: Jacques Neveu appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Jacques Neveu in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Jacques Neveu is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1932 births, 2016 deaths, Academic staff of the University of Paris, so understanding it makes those chapters shorter.
In everyday life: Look for Jacques Neveu outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Jacques Neveu in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Jacques Neveu means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Jacques Neveu out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Jacques Neveu in simple terms?

Why does Jacques Neveu matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Jacques Neveu?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Jacques Neveu.