162 citations · 848 across the 46 of their papers we have counts for
46 papers · 1 filter
Norm of matrix-valued polynomials in random unitaries and permutations
Charles Bordenave, Benoit Collins
We consider a non-commutative polynomial in several independent -dimensional random unitary matrices, uniformly distributed over the unitary, orthogonal or symmetric groups, and…
Mobility Edge for Lévy Matrices
Amol Aggarwal, Charles Bordenave, Patrick Lopatto
Lévy matrices are symmetric random matrices whose entry distributions lie in the domain of attraction of an -stable law. For , predictions from the physics literature sugg…
Noise sensitivity for the top eigenvector of a sparse random matrix
Charles Bordenave, Jaehun Lee
We investigate the noise sensitivity of the top eigenvector of a sparse random symmetric matrix. Let be the top eigenvector of an sparse random symmetric matrix wit…
Existence of absolutely continuous spectrum for Galton-Watson random trees
Adam Arras, Charles Bordenave
We establish a quantitative criterion for an operator defined on a Galton-Watson random tree for having an absolutely continuous spectrum. For the adjacency operator, this criterio…
Typicality and entropy of processes on infinite trees
Ágnes Backhausz, Charles Bordenave, Balázs Szegedy
Consider a uniformly sampled random -regular graph on vertices. If is fixed and goes to then we can relate typical (large probability) properties of such ra…
Strong asymptotic freeness for independent uniform variables on compact groups associated to non-trivial representations
Charles Bordenave, Benoit Collins
Asymptotic freeness of independent Haar distributed unitary matrices was discovered by Voiculescu. Many refinements have been obtained, including strong asymptotic freeness of rand…