# Jacques Jean-Pierre Joseph Neveu

### Quick Info

Born
14 November 1932
Watermael-Boitsfort, near Brussels, Belgium
Died
15 May 2016
Paris, France

### Biography

Jacques Neveu was born and brought up in Belgium. He was born in Watermael-Boitsfort which is the French version of its name while the Dutch version of this town is Watermaal-Bosvoorde. It is now a residential suburb of the city of Brussels and is now, therefore, legally bilingual French/Dutch. The double name comes from the merging of two towns in the early 19th century.

Neveu went to France for university studies and continued to live in France for the rest of his life. He became a naturalised French citizen on 3 June 1965. His interests turned towards probability theory and he undertook research at the University of Paris advised by Robert Fortet. Fortet (1912-1998) had been a student of Maurice Fréchet and had been awarded a doctorate in 1939 for his thesis Sur l'itération des substitutions algébriques linéaires à une infinité de variables et ses applications à la théorie des probabilités en chaîne . Neveu was awarded his doctorate in 1955 for his thesis Etude des semi-groupes de Markoff . He began publishing in 1955 and three of his papers appeared in that year, namely: Sur une hypothèse de Feller à propos de l'équation de Kolmogoroff ; Semi-groupes généralisés et processus de Markoff ; and Jeux de Markoff et problèmes d'absorption .

It was in Paris that Neveu worked for the whole of his career beginning at the Faculty of Science. Along with Fortet, he was among the first members of the Laboratoire de Probabilités et Modèles Aléatoires in 1960. Neveu became a lecturer at the Collège de France in 1962. Various changes, however, to the University of Paris meant that he was forced to make certain decisions about where he would work. We will discuss these below but first we look at various visits that Neveu made to the United States in the 1960s.

In 1961 he attended the 4th Berkeley Symposium on Mathematical Statistics and Probability and contributed the paper Lattice methods and submarkovian processes which was published in the Proceedings of the Conference.

The American Mathematical Society records his visit to Berkeley in 1965 [14]:-
In 1965 Belgian-born French mathematician Jacques Neveu (1932-2016) was in Berkeley teaching a course in modern probability theory. His time in the United States inspired generous gifts to the American Mathematical Society. "It is a great pleasure for me to contribute to the remarkable work done by the American Mathematical Society with the remembrance for all the marvellous contacts I have had with the American mathematical community," he wrote the American Mathematical Society in 2006.
Neveu was in Berkeley to attend the Berkeley Symposium on Mathematical Statistics and Probability held in 1965-66. He contributed the paper Existence of bounded invariant measures in ergodic theory. He gives his address on the paper as University of Paris and University of California Berkeley. The paper has a one sentence Introduction:-
We present a survey of some recent work done on the problem of existence of bounded invariant measure for positive contractions defined on $L^{1}$-spaces.
Let us return to the story of the splitting of the University of Paris into thirteen separate universities in 1970. Here is Michel Zisman's description of how these changes affected Neveu [16]:-
I met Jacques Neveu at a very special moment in the history of Parisian universities, 1969-71, where the only University of Paris with its headquarters at the Sorbonne gave birth to the thirteen universities that we know today. Jacques ... closely followed the painful and complex upheavals that accompanied the birth of the two French universities, Paris VI and Paris VII, which, with regard to mathematics, belonged to the old IHP, the Henri Poincaré Institute. Often, at the foot of the towers of Jussieu, we discussed the future that was open to us, our ability to act, to help guide it according to our ideal. At the time, the Mathematics Department of the University of Paris had a two-headed management, each of the two heads representing one of the two universities in the making, and I was, on François Bruhat's initiative, one of those two. At that time, my discussions with Jacques revolved around what would happen to this still planned university, to which Bruhat would devote ten years of his life. In principle, teachers were free to choose their university, but in practice the choice of the laboratory head determined that of his colleagues, and so Jacques, following R Fortet, found himself in Paris VI where, he told me, he was not happy; so, as soon as he could, he went to the École Polytechnique.
Francis Comets tell us about Neveu's teaching in [3]:-
As a lecturer at the Paris Faculty of Sciences, Paris VI University and the École Polytechnique, he took great pleasure and care in his teaching, and he shared his passion with several generations of probabilists, scientists and engineers with varied vocations. His classes were always luminous, wonderfully compact, and full of that elegance that made his books get so many references today.
With this mention of his books, we should say something about them. They include Théorie des semi-groups de Markov (1958), Bases mathématiques du calcul des probabilités (1964), Mathematical foundations of the calculus of probability (1965), Processus aléatoires gaussiens (1968), Martingales à temps discret (1972), and Discrete-parameter martingales (1975). The books with English titles are translations of the earlier French ones.

For extracts from reviews of some of these works, as well as other information about them, see THIS LINK.

Let us record here a very brief extract from [4] which is typical of the praise reviewers have for Neveu's books:-
This is an excellent book by a brilliant mathematician, expertly and beautifully translated into English. As a text it is intended for study by advanced students (corresponding roughly to the first or second year of graduate work in probability or measure theory in the United States and Canada) and as a reference work for researchers. There is no doubt that it will succeed brilliantly in fulfilling these aims.
To gain an appreciation of Neveu's outstanding research, we quote again from Francis Comets [3]:-
From the beginning of his career his impact on the mathematical community and the French school of probability is obvious and striking, at a time when applied mathematics and probability theory in particular are still gaining ground. The first seminars he conducted in Paris stimulated a whole generation of young probabilists, implicitly in tandem with Paul-André Meyer and the Strasbourg School. All along, he played a central role in the development of probability theory, especially through the working groups he led in a lively way. His research is one of the most beautiful pages of probability theory: Markov chains and processes, Gaussian processes, ergodic theory, potential theory, martingales, point measurements, random trees and branching processes. Beyond the fundamental aspects, he also contributed to the development of applications. In the field of stochastic networks, his founding works as well as the reading group he led on this subject at the end of the 70s, structured the French community. Subsequently, he contributed to the links with fundamental computing, combinatorics and statistical physics. He also founded the group "Modélisation Aléatoire et Statistique" of the Société de Mathématiques Appliquées et Industrielles [in 1991].
Michel Zisman explains in [16] that after Neveu left the Paris VI University and worked in the École Polytechnique:-
... we did not see each other anymore; it should have been the end of our friendship: chance decided otherwise. My wife owns a small family home in La Ripe, a hamlet of ten inhabitants above the Yonne, where we spent all our holidays. We did our shopping in Mailly-le-Château, on the other side of the Yonne. One day we meet Jacques and his wife, Monique, at the baker's! The Neveus had bought a beautiful property in this Burgundy village, three kilometres from us. A beautiful mansion, a beautiful flower garden terrace on the back overlooking the river and, on the other side of the street, a vegetable garden. In the living room, Jacques had installed a magnificent fireplace built to his plans, in which he liked to burn tree trunks of good size, for the great joy of his guests when the weather was cool. It was in this context that Jacques discovered a new passion. He had always liked to cook, and he cooked very well; he now cooked the vegetables and fruits of his own garden. Depending on the season, turning over the land, pruning trees or roses, preparing seedlings, harvesting strawberries or leeks, he was always at work! Difficult to leave this welcoming home without taking a jar of plum jam or jelly.

Other academics, scientists: some renowned archaeologists, physicists, curators of the Louvre Museum, chose to buy a second home in Mailly-le-Château and found themselves around the Neveus. This peaceful village, two hours from Paris, which for decades evoked angling in the Yonne or climbing on the cliffs of Saussois and was known around the world for high places for climbing became unknowingly the seat of a curious literary set where the quality of the cuisine of Jacques and Monique disputed with the richness of the conversation!

These happy days are a thing of the past. With the coming of age and the accumulating fatigue, Jacques had to call on a professional to execute the heavy work in his gardens. Their beautiful house in Mailly-le-Château was closed all year in 2015. Monique died of cancer and Jacques followed soon after her. A few days before his death, he called me to tell me he was in the hospital ...
Neveu was honoured with being elected to the Inaugural Class of Fellows of the American Mathematical Society in 2013. He was elected president of the Société Mathématique de France for 1977-78. The group which he founded, the "Modélisation Aléatoire et Statistique" of the Société de Mathématiques Appliquées et Industrielles, inaugurated a prize awarded to the person judged to have the best doctoral dissertation in mathematicians or statistics in France in the year of the award. Special attention is given to theses having important links with other fields (life science, material science, engineering science, physical sciences, ... or a strong involvement in the dissemination of knowledge to the industrial field. It was first awarded in 2008.

Let us leave the final comment to Francis Comets [3]:-
His work in the Probability Laboratory at Jussieu and the Centre for Applied Mathematics at the École Polytechnique remains an example of clairvoyance, generosity and discernment. Friendly and considerate, of a great culture and sensitivity, his company was sought after. Like many of us, I have a very vivid memory of Jacques Neveu's quick intelligence, of his inexhaustible taste for rigour, for the elegance of his thought.

### References (show)

1. R M Blumenthal, Review: Mathematical foundations of the calculus of probability, by Jacques Neveu, Annals of Mathematical Statistics 38 (2) (1967), 624-625.
2. D L Burkholder, Review: Martingales à temps discret (1972), by Jacques Neveu, Mathematical Reviews MR0402914 (53 #6728).
3. F Comets, Jacques Neveu (1932-2016), Société Mathematique de France (23 May 2006). https://smf.emath.fr/sites/default/files/old_site/jacques_neveu-smf.pdf
4. M Csörgö, Review: Mathematical foundations of the calculus of probability, by Jacques Neveu, Canadian Math. Bull. 10 (2) (1967), 308.
5. D A Darling, Review: Discrete-parameter martingales, by Jacques Neveu, Bull. Amer. Math. Soc. 82 (6) (1976), 836-840.
6. Décès de Jacques Neveu, Société Mathematique de France (23 May 2006). https://smf.emath.fr/actualites-smf/deces-de-jacques-neveu
7. C Doléans-Dade, Review: Martingales à temps discret (1972), by Jacques Neveu, SIAM Review 16 (3) (1974), 398-399.
8. F Eicker, Review: Mathematical foundations of the calculus of probability, by Jacques Neveu, SIAM Review 9 (1) (1967), 136-139.
9. Hommage à Jacques Neveu (1932-2016), Le Centre national de la recherche scientifique, Institut national des sciences mathématique et leur interactions (9 June 2016). https://www.cnrs.fr/insmi/spip.php?article1748
10. Jacques Neveu (1932-2016), American Mathematical Society (7 July 2016). http://www.ams.org/news?news_id=3111
11. D G Kendall, Review: Bases mathématiques du calcul des probabilités, by Jacques Neveu, The Mathematical Gazette 50 (371) (1966), 82-83.
12. J F C Kingman, Review: Mathematical foundations of the calculus of probability, by Jacques Neveu, Journal of the Royal Statistical Society. Series A (General) 129 (3) (1966), 475-476.
13. M Loève, Review: Processus aléatoires gaussiens, by Jacques Neveu, Mathematical Reviews MR0272042 (42 #6923).
14. Mathematical lives - Jacques Neveu, The Line 7 (American Mathematical Society, 2016).
15. S Orey, Review: Bases mathématiques du calcul des probabilités, by Jacques Neveu, Mathematical Reviews MR0198504 (33 #6659).
16. M Zisman, Jacques Neveu jardinier, Société Mathematique de France (23 May 2006). https://smf.emath.fr/sites/default/files/old_site/jacques_neveu_jardinier.pdf