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# Joseph Najnudel

Email: najnudjh@ucmail.uc.edu

## Education

• PhD, Université Paris VI, Paris, 2007 (Probability theory).

## Research Information

### Research Interests

• Random matrix theory: study of random unitary matrices (in particular the Circular Unitary Ensemble), random permutation matrices and related infinite-dimensional limiting objects, link between random matrix theory and number theory.
• Stochastic analysis: study of limiting measures constructed by modifying the Brownian motion or more general stochastic processes, study of the Brownian local times and polymer models.

## Publications

### Peer-reviewed Publications

• R. Chhaibi, J. Najnudel, A. Nikeghbali (2017). The Circular Unitary Ensemble and the Riemann zeta function: the microscopic landscape and a new approach to ratios. Inventiones Math., 207 (1), 23-113.
• J. Najnudel, A. Nikeghbali, A. Rouault (2016). Limit theorems for orthogonal polynomials related to circular ensembles. Journal of Theoretical Probability, 29 (4), 1199-1239.
• Y. Barhoumi-Andreani, C. Hughes, J. Najnudel, A. Nikeghbali (2015). On the number of zeros of linear combinations of independent characteristic polynomials of random unitary matrices. Intern. Math. Research Notices, 2015, 12366-12404.
• E. Kowalski, J. Najnudel, A. Nikeghbali (2015). A characterization of limiting functions arising in mod-* convergence. Elec. Comm. in Probab., 20 (79), 1-11.
• C. Hughes, J. Najnudel, A. Nikeghbali, D. Zeindler (2013). Random permutation matrices under the generalized Ewens measure. Annals of Applied Probability, 23 (3), 987-1024.
• J. Najnudel, A. Nikeghbali (2013). The distribution of eigenvalues of randomized permutation matrices. Ann. Inst. Fourier, 63 (3), 773-838.
• J. Najnudel, A. Nikeghbali (2013). On penalisation results related with a remarkable class of submartingales. Markov Proc. and Rel. Fields, 19 (4), 763-790.
• J. Najnudel, A. Nikeghbali (2012). On some universal sigma-finite measures related to a remarkable class of submartingales. Stochastic Process. and their Appl., 122 (4), 1582-1600.
• J. Najnudel, D. Stroock, M. Yor (2012). On a flow of transformations of a Wiener space. pringer Proceedings in Mathematics and Statistics, 22, 119-131.
• P. Bourgade, J. Najnudel, A. Nikeghbali (2012). A unitary extension of virtual permutations. International Math. Research Notices, 2013 (18), 4101-4134.
• J. Najnudel, A. Nikeghbali (2011). A new kind of augmentation of filtrations. ESAIM: Probability and Statistics, 15, S39-S57.
• J. Najnudel, A. Nikeghbali (2011). On some properties of a universal sigma-finite measure associated with a remarkable class of submartingales. Publ. RIMS Kyoto Univ., 47, 911-936.
• J. Najnudel, A. Nikeghbali (2010). A new construction of the sigma-finite measures associated with submartingales of class Sigma. C. R. Math. Acad. Sci. Paris, 348, 311-316.
• J. Najnudel (2010). Construction of an Edwards' probability measure on C(R_+,R). Annals of Probability, 38 (6), 2295-2321.
• J. Najnudel, A. Nikeghbali, F. Rubin (2009). Scaled limit and rate of convergence for the largest eigenvalue from the generalized Cauchy random matrix ensemble. Journal of Statistical Physics, 137 (2), 373-406.
• J. Najnudel (2008). Penalizations of the Brownian motion by a functional of its local times. Stochastic Process. and their Appl., 118 (8), 1407-1433.
• J. Najnudel, B. Roynette, M. Yor (2007). A remarkable sigma-finite measure on C(R+,R) related to many Brownian penalisations. C. R. Math. Acad. Sci. Paris, 345 (8), 459-466.
• J. Najnudel (2007). Pénalisations de l'araignée brownienne (Penalizations of the Brownian spider). Ann. Inst. Fourier, 57 (4), 1063-1093.

### Published Books

• J. Najnudel, B. Roynette, M. Yor (2009). A global view of Brownian penalisations. MSJ Memoirs, Mathematical Society of Japan, Volume 19.

### Book Chapters

• J. Najnudel (2015). On sigma-finite measures related to the Martin boundary of recurrent Markov chains. Séminaire de probabilités XLVII, in memoriam Marc Yor (pp.263-297). Springer.
• J. Najnudel, A. Nikeghbali (2014). On a flow of operators associated to virtual permutations. Séminaire de probabilités XLVI (pp.481-512). Springer.
• J. Najnudel, A. Nikeghbali (2010). A remarkable sigma-finite measure associated with last passage times and penalisation problems. Contemporary Quantitative Finance, Essays in Honour of Eckhard Platen (pp.77-98). Springer.
• J. Najnudel (2007). Integration with respect to self-intersection local time of a one-dimensional Brownian motion. Séminaire de probabilités XL (pp.105-116). Springer.

### Other Publications

• J. Najnudel (2017). On consecutive values of random completely multiplicative functions. Preprint.
• R. Chhaibi, T. Madaule, J. Najnudel (2016). On the maximum of the C$\beta$E field. Preprint.
• J. Najnudel (2016). On the extreme values of the Riemann zeta function on random intervals of the critical line. Preprint. To appear in Prob. Th. and Rel. Fields.
• R. Chhaibi, J. Najnudel, A. Nikeghbali (2014). A limiting random analytic function related to the CUE. Preprint.
• K. Maples, J. Najnudel, A. Nikeghbali (2013). Limit operators for circular ensembles. Preprint.
• J. Najnudel (2007). Temps locaux et pénalisations browniennes (local times and Brownian penalisations). PhD thesis.

## Honors & Awards

• Two gold medals at the International Mathematical Olympiad, 1997 to 1998.

## Experience & Service

### Work Experience

• 08-2016 to To Present, Assistant Professor, University of Cincinnati.
• 09-2012 to 08-2016, Maître de conférences, Université Paul Sabatier Toulouse III.
• 06-2008 to 05-2012, Lecturer, Universität Zürich.
• 03-2008 to 05-2008, Post-doctorant, Universität Zürich.
• 09-2007 to 02-2008, Post-doctorant, ETH Zürich.
• 12-2003 to 08-2007, PhD student, Université Paris VI.

### Events Organized

• Workshop on random matrices (04-15-2010 to 04-16-2010) , Zürich.
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