4 papers · 1 filter
Sparse graphs and their Benjamini-Schramm limits: a spectral tour
Charles Bordenave
Sparse graphs with bounded average degree form a rich class of discrete structures where local geometry strongly influences global behavior. The Benjamini-Schramm (BS) convergence…
Cutoff for geodesic paths on hyperbolic manifolds
Charles Bordenave, Joffrey Mathien
We establish new instances of the cutoff phenomenon for geodesic paths and for the Brownian motion on compact hyperbolic manifolds. We prove that for any fixed compact hyperbolic m…
Outliers of perturbations of banded Toeplitz matrices
Charles Bordenave, François Chapon, Mireille Capitaine
Toeplitz matrices form a rich class of possibly non-normal matrices whose asymptotic spectral analysis in high dimension is well-understood. The spectra of these matrices are notor…
Large deviations for macroscopic observables of heavy-tailed matrices
Charles Bordenave, Alice Guionnet, Camille Male
We consider a finite collection of independent Hermitian heavy-tailed random matrices of growing dimension. Our model includes the Lévy matrices proposed by Bouchaud and Cizeau, as…