P A U L    B O U R G A D E  Courant


My research interests lie in probability, in particular random matrices and statistical physics.

 
 Events
The Courant Institute probability seminar.
2024, August 26-28. Advances in probability theory and interacting particle systems, a conference in honor of S. R. Srivinasa Varadhan.
 
Previously
 
Research
Optimal rigidity and maximum of the characteristic polynomial of Wigner matrices, with P. Lopatto and O. Zeitouni, 2023.
The Fyodorov-Hiary-Keating Conjecture. II, with L. P. Arguin and M. Radziwill, 2023.
Liouville quantum gravity from random matrix dynamics, with H. Falconet, 2022.
Landscape complexity beyond invariance and the elastic manifold, with G. Ben Arous and B. McKenna, to appear in Communications on Pure and Applied Mathematics, 2021.
Exponential growth of random determinants beyond invariance, with G. Ben Arous and B. McKenna, to appear in Probability and Mathematical Physics, 2021.
Optimal local law and central limit theorem for β-ensembles, with K. Mody and M. Pain, Comm. Math. Phys. 390, no. 3, 1017-1079, 2022.
The Fyodorov-Hiary-Keating conjecture. I, with L. P. Arguin and M. Radziwill, 2020.
Extreme gaps between eigenvalues of Wigner matrices, Journal of the European Mathematical Society, vol. 24, no. 8, 2823-2873, 2022.
Gaussian fluctuations of the determinant of Wigner Matrices, with K. Mody, Electronic Journal of Probability, Volume 24, no 96, 2019.
Random band matrices in the delocalized phase, II: Generalized resolvent estimates, with F. Yang, H.-T. Yau and J. Yin, Journal of Statistical Physics, vol. 174, 1-33, 2019.
Random band matrices in the delocalized phase, I: Quantum unique ergodicity and universality, with H.-T. Yau and J. Yin, Communications on Pure and Applied Mathematics, vol. 13, no. 7, 1526-1596, 2020.
The distribution of overlaps between eigenvectors of Ginibre matrices, with G. Dubach, Probability Theory and Related Fields, vol. 177, 397-464, 2020.
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, Communications on Pure and Applied Mathematics, volume 72, issue 3, 500-535, 2019.
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, Advances in Theoretical and Mathematical Physics, vol. 23, no.4, 2019.
Universality for a class of random band matrices, with L. Erdős, H.-T. Yau and J. Yin, Advances in Theoretical and Mathematical 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, Journal of Mathematical Physics, 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 between 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, International Mathematical 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'Academie des Sciences, 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 Mathematical 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 internationales de mathématiques, published by the éditions Cassini (in French, 2005).
 
Teaching
Spring 2024Undergraduate complex analysis
Previous terms

Contact

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

Here is my curriculum vitae.