152 citations · 743 across the 29 of their papers we have counts for
3 papers · 2 filters
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…