152 citations · 743 across the 29 of their papers we have counts for
31 papers · 1 filter
Liouville quantum gravity from random matrix dynamics
Paul Bourgade, Hugo Falconet
We establish the first connection between Liouville quantum gravity and natural dynamics of random matrices. In particular, we show that if is a Brownian motion on the…
Landscape complexity beyond invariance and the elastic manifold
Gérard Ben Arous, Paul Bourgade, Benjamin McKenna
This paper characterizes the annealed, topological complexity (both of total critical points and of local minima) of the elastic manifold. This classical model of a disordered elas…
Exponential growth of random determinants beyond invariance
Gérard Ben Arous, Paul Bourgade, Benjamin McKenna
We give simple criteria to identify the exponential order of magnitude of the absolute value of the determinant for wide classes of random matrix models, not requiring the assumpti…
Optimal local law and central limit theorem for -ensembles
Paul Bourgade, Krishnan Mody, Michel Pain
In the setting of generic -ensembles, we use the loop equation hierarchy to prove a local law with optimal error up to a constant, valid on any scale including microscopic. This…
The Fyodorov-Hiary-Keating Conjecture. I
Louis-Pierre Arguin, Paul Bourgade, Maksym Radziwiłł
By analogy with conjectures for random matrices, Fyodorov-Hiary-Keating and Fyodorov-Keating proposed precise asymptotics for the maximum of the Riemann zeta function in a typical…
Extreme gaps between eigenvalues of Wigner matrices
Paul Bourgade
This paper proves universality of the distribution of the smallest and largest gaps between eigenvalues of generalized Wigner matrices, under some smoothness assumption for the den…