P A U L    B O U R G A D E  Courant


My research interests lie in probability, in particular random matrices, statistical physics, their links with analytic number theory, and stochastic processes.

During the 2018-2019 year, my work is sponsored by the Poincaré chair and the National science foundation.

Teaching
Spring 2018Random Matrix Theory
Fall 2017Stochastic Analysis
Previous terms
Research
Random band matrices in the delocalized phase, II: Generalized resolvent estimates, with F. Yang, H.-T. Yau and J. Yin, prepublication, 2018.
Random band matrices in the delocalized phase, I: Quantum unique ergodicity and universality, H.-T. Yau and J. Yin, prepublication, 2018.
The distribution of overlaps between eigenvectors of Ginibre matrices, with G. Dubach, prepublication, 2018.
Maximum of the Riemann zeta function on a short interval of the critical line, with L. P. Arguin, D. Belius, M. Radziwill and K. Soundararajan, to appear in CPAM, 2018.
Eigenvector Statistics of Sparse Random Matrices, with J. Huang and H.-T. Yau, Electronic Journal of Probability, vol. 22, no. 64, 2017.
The two-dimensional Coulomb plasma: quasi-free approximation and central limit theorem, with R. Bauerschmidt, M. Nikula and H.-T. Yau, prepublication, 2016.
Universality for a class of random band matrices, with L. Erdős, H.-T. Yau and J. Yin, Advances in Theor and Math Physics, vol. 21, no. 3, 739-800, 2017.
Maximum of the characteristic polynomial of random unitary matrices, with L. P. Arguin and D. Belius, Communications in Mathematical Physics, vol. 349, no. 2, 703-751, 2017.
Local density for two-dimensional one-component plasma, with R. Bauerschmidt, M. Nikula and H.-T. Yau, Communications in Mathematical Physics, vol. 356, 189-230, 2017.
Fixed energy universality for generalized Wigner matrices, with L. Erdős, H.-T. Yau and J. Yin, Communications on Pure and Applied Mathematics, vol. 69, no. 10, 1815-1881, 2016.
The eigenvector moment flow and local quantum unique ergodicity, with H.-T. Yau, Communications in Mathematical Physics, vol. 150, no. 1, 231-278 2017.
Edge Universality of β-ensembles, with L. Erdős and H.-T. Yau, Communications in Mathematical Physics, vol. 332, no. 1, 261-353, 2014.
The local circular law II: the edge case, with H.-T. Yau and J. Yin, Probability Theory and Related Fields, vol. 159, no. 3-4, 619-660, 2014.
The local circular law for random matrices, with H.-T. Yau and J. Yin, Probability Theory and Related Fields, vol. 159, no. 3-4, 545-595, 2014.
Strong Szegő asymptotics and zeros of the ζ  function, with J. Kuan, Communications on Pure and Applied Mathematics, vol. 67, mo. 6, 1028–1044, 2014.
Bulk universality of general β-ensembles with non-convex potential, with L. Erdős and H.-T. Yau, J. of Math. Phys., special issue in honor of E. Lieb's 80th birthday, vol. 53, 2012.
Universality of general β-ensembles , with L. Erdős and H.-T. Yau, Duke Mathematical Journal vol. 163, no. 6, 1127-1190, 2014.
Extreme gaps in the eigenvalues of random matrices , with G. Ben Arous, Annals of Probability, vol. 41, no. 4, 2648-2681, 2013.
A unitary extension of virtual permutations, with J. Najnudel and A. Nikeghbali, Int. Math. Research Notices vol. 2013, no. 18, 4101–4134, 2013.
Mesoscopic fluctuations of the ζ zeros, Probability Theory and Related Fields, Volume 148, Numbers 3-4, 479-500, 2010.
Circular Jacobi ensembles and deformed Verblunsky coefficients, with A. Nikeghbali and A. Rouault, International Mathematical Research Notices, Vol. 2009, no. 23, 4357-4394.
Conditional Haar measures on classical compact groups, Annals of Probability vol 37, no. 4, 1566-1586, 2009.
Ewens measures on compact groups and hypergeometric kernels, with A. Nikeghbali and A. Rouault, Séminaire de Probabilités XLIII, 351-377, Springer, 2011.
The characteristic polynomial on compact groups with Haar measure: some equalities in law, with A. Nikeghbali and A. Rouault, Comptes Rendus de l'Ac. des Sc., 345, 4, 2007.
Euler's formula for ζ(2n) and products of Cauchy variables, with T. Fujita and M. Yor, Electronic Communications in Probability 12, 73-80, 2007.
The characteristic polynomial of a random unitary matrix: a probabilistic approach, with C.P. Hughes, A. Nikeghbali and M. Yor, Duke Math. Journal vol 145, no. 1, 45-69, 2008.
Various texts
Random band matrices, proceedings of the International Congress of Mathematicians, 2018.
Stochastic Analysis, lecture notes from my graduate course given in Fall 2010 at Harvard and Fall 2016 at Courant.
Marc Yor et les matrices aléatoires, numéro spécial de la Gazette des mathématiciens (in French, 2015).
Quantum chaos, random matrix theory, and the Riemann ζ  function , with J. Keating, proceedings of the Séminaire Poincaré, Birkhauser, Chaos Progress in Mathematical Physics, vol. 66, 2013, 125-168, 2013.
Bulk universality for one-dimensional log-gases, proceedings of the XVIIth International Congress On Mathematical Physics, World Scientific Publishing, 2013.
Tea time in Princeton, an expository article about the analogies between the statistics of random eigenvalues and zeros of L-functions, Harvard College Math. Review (2012).
On random matrices and L-functions, my Ph.D. thesis, under supervision of M. Yor (this version: 2010).
Lois de Poisson-Dirichlet, my senior thesis, about the occurrences of this measure for excursions and the distribution of large prime factors (in French, 2007).
Annales des Olympiades internationnales de mathématiques, published by the éditions Cassini (in French, 2005).
Conferences
Seminars
The NYU Probability and Mathematical Physics Seminar.
The 2018 Northeast probability seminar.
From Many Body Problems to Random Matrices, a workshop in honor of H.-T. Yau for his 60th birthday (2019).
Dynamics, aging and universality in complex systems, a conference in honor of G. Ben Arous for his 60th birthday (2017).
The Harvard Probability Seminar.
Random Matrices, Random Geometry, a joint Harvard-MIT probability afternoon.
The conference in honor of A.S. Üstünel for his 60th birthday.
The Random Matrices conference, at Institut Henri Poincaré.
The Stochastic Analysis seminar, at Institut Henri Poincaré.

Contact

email
bourREMOVETHISTEXTgade@cims.nyu.edu
address
251 Mercer Street
New York, NY 10012-1185, USA

Here is my curriculum vitae.