Random matrix models and their infinite-dimensional generalizations. Stochastic processes, filtrations and applications to mathematical finance.

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1 Joseph Najnudel Institut de mathématiques de Toulouse - Université Paul Sabatier 118, route de Narbonne, F Toulouse Cedex 9 Tel. : joseph.najnudel at math.univ-toulouse.fr Nationality: French Born Research interests Random matrix models and their infinite-dimensional generalizations. Stochastic processes, filtrations and applications to mathematical finance. Limiting probability measures constructed from the Brownian motion. Polymer models. Publications The following papers concern random matrix models and some of their infinite-dimensional generalizations: K. Maples, J. Najnudel, A. Nikeghbali: Limit operators for circular ensembles. Preprint (2013). E. Kowalski, J. Najnudel, A. Nikeghbali: A characterization of limiting functions arising in mod-* convergence. Preprint (2013). J. Najnudel, A. Nikeghbali, A. Rouault: Limit theorems for orthogonal polynomials related to circular ensembles. Preprint (2013). Y. Barhoumi, C. Hughes, J. Najnudel, A. Nikeghbali: On the number of zeros of linear combinations of independent characteristic polynomials of random unitary matrices. Preprint (2013). J. Najnudel, A. Nikeghbali: On a flow of operators associated to virtual permutations. To appear in Séminaire de Probabilités.

2 C. Hughes, J. Najnudel, A. Nikeghbali, D. Zeindler: Random permutation matrices under the generalized Ewens measure. Annals of Applied Probability, Volume 23, no. 3, pp (2013). J. Najnudel, A. Nikeghbali: The distribution of eigenvalues of randomized permutation matrices. Annales de l institut Fourier, Volume 63, no. 3, pp (2013). P. Bourgade, J. Najnudel, A. Nikeghbali: A unitary extension of virtual permutations. International Math. Research Notices, Volume 2013, no. 18, pp (2012). J. Najnudel, A. Nikeghbali, F. Rubin: Scaled limit and rate of convergence for the largest eigenvalue from the generalized Cauchy random matrix ensemble. Journal of Statistical Physics, Volume 137, no. 2, pp (2009). My main result on polymer models is given in the following article: J. Najnudel: Construction of an Edwards probability measure on C(R+,R). Annals of Probab., Volume 38, no. 6, pp (2010). In the following articles, we study a family of σ-finite measures associated to a remarkable class of submartingales. Some of the results which are obtained are related to problems in mathematical finance. J. Najnudel, A. Nikeghbali: On penalisation results related with a remarkable class of submartingales. To appear in Markov Processes and Related Fields. J. Najnudel, A. Nikeghbali: On some universal sigma-finite measures and some extensions of Doob s optional stopping theorem. Stochastic Process. Appl., Volume 122, no. 4, pp (2012). J. Najnudel, A. Nikeghbali: On some properties of a universal sigmafinite measure associated with a remarkable class of submartingales. Publ. RIMS Kyoto Univ., Volume 47, pp (2011).

3 J. Najnudel, A. Nikeghbali: A new kind of augmentation of filtrations. ESAIM: Probability and Statistics, Volume 15, pp. S39 S57 (2011). J. Najnudel, A. Nikeghbali: A remarkable σ-finite measure associated with last passage times and penalisation problems. Contemporary Quantitative Finance, Essays in Honour of Eckhard Platen, pp , Springer (2010). J. Najnudel, A. Nikeghbali: A new construction of the σ-finite measures associated with submartingales of class (Σ). C. R. Math. Acad. Sci. Paris, Volume 348, pp (2010). The following papers are related to the topic of my PhD thesis (local times and Brownian penalizations): J. Najnudel, D. Stroock, M. Yor: On a flow of transformations of a Wiener space. Preprint (2011). To appear in: Proceedings of the 9th workshop on stochastic analysis and related fields. J. Najnudel, B. Roynette, M. Yor: A global view of Brownian penalisations. MSJ Memoirs, Mathematical Society of Japan, Volume 19 (2009). J. Najnudel: Penalizations of the Brownian motion by a functional of its local times. Stochastic Process. Appl., Volume 118, no. 8, pp (2008). J. Najnudel, B. Roynette, M. Yor: A remarkable sigma-finite measure on C(R+,R) related to many Brownian penalisations. C. R. Math. Acad. Sci. Paris, Volume 345, no. 8, pp (2007). J. Najnudel: Temps locaux et pénalisations browniennes (local times and Brownian penalisations). PhD thesis (2007). J. Najnudel: Pénalisations de l araignée brownienne (Penalizations of the Brownian spider). Ann. Inst. Fourier (Grenoble), Volume 57, no. 4, pp (2007). J. Najnudel: Integration with respect to self-intersection local time of a one-dimensional Brownian motion. Séminaire de Probabilités, Volume XL, pp , Lecture Notes in Math. 1899, Springer, Berlin, 2007.

4 Employment present Maître de Conférences at the Université Paul Sabatier, Toulouse Lecturer at the University of Zurich Postdoctorant at the University of Zurich, in the working group of Prof. Bolthausen Postdoctorant at the ETH Zurich, in the working group of Prof. Sznitman. Scientific education Defense of my habilitation à diriger des recherches, at the University Paris VI (France): a diploma which allows to apply for a professorship in France PhD student at the University Paris VI, under the supervision of Prof. Yor (defense in June 2007) Student at the Ecole Normale Supérieure of Paris Agrégation de Mathématiques, the most prestigious french competition selecting people on their ability to teach (rank 1) DEA (Diploma of Advanced Studies, 2nd year of Master s Degree), in probability theory (stochatstic processes), University Paris VI Maîtrise in Mathematics (1st year of Master s Degree), University Paris VI Preparatory classes at the lycée Louis le Grand (Paris). Teaching activity Convergence of probability measures and large deviations, a fifth year (master 2) course, for students planning to do research in mathematics General course in mathematics for first year students preparing competition to enter in engineering schools.

5 General course in mathematics for third year students in economics Stochastic simulation (course and exercises), a third year course where I teach the methods of simulation of random variables and Markov processes, the Monte- Carlo methods, etc. The students are programming in Matlab Stochastic processes and their applications, Berlin Probability theory (course, and organization of the exercise classes with the assistants). This course is the first probabilistic course for the students, from the second year level Introduction to mathematical finance (course and exercises), second year level and higher Calculus and introduction to number theory (exercises), at first and second year levels. Activity of supervision 2015 Two master theses (M2), one by a student applying for a PhD under my supervision Supervision of a bachelor (L3) project, on the coin tossing Supervision of a master thesis (M2) on the asymptotics of random permutations (defense in September 2013). Main recent talks Séminaire de Probabilités, Université de Strasbourg (two talks) Probability seminar, Fields Institue, Toronto Séminaire de Probabilités, Université de Strasbourg Colloquium, Mathematisches Institut, Universität Freiburg Séminaire de Probabilités, Université de Strasbourg Probability seminar, Fields Institute, Toronto.

6 Seminar über stochastische Prozesse, probability seminar of the ETH and the University of Zurich Disentis summer school, Switzerland Probability seminar, Fields Institute, Toronto Workshop on Random Matrices, University of Zurich Stochastic processes and their applications, Berlin Conference in honor of the 60th birthday of Marc Yor, Institut Henri Poincaré, Paris Conference on random matrices ( Journées Matrices Aléatoires ), Insititut Henri Poincaré, Paris Conference Random matrices, L-functions and primes, ETH Zurich Disentis summer school, Switzerland Séminaire de Probabilités, Institut Fourier, Grenoble Symposium in Mathematics, University of Zurich. Events Organization, with Prof. Nikeghbali, of the conference: Workshop on Random Matrices, at the University of Zurich Teaching at a summer school organized by the Bocconi university (Italy): 30 hours of lecture and exercises on the topic of my PhD Mini-course at the university of Warwick (UK). Languages French: mother tongue. English: fluent. German: B1 certificate of the Goethe Institute. Music I play the piano in a very intensive way. Between 1997 and 2007, I was a student at the Conservatory of Paris, where I have obtained several prizes and awards. I am regularly doing concerts of classical music, and I have composed many works for piano.