9 papers
A sandwich theorem for the spectrum of graph coverings
Charles Bordenave, Wenbo Li, Joe Thomas
We show that all normal covers of a fixed finite graph sitting between the universal and maximal abelian covers share the same atomic part of their spectral measures. We give a…
Logarithmic regularity of spectral measures on infinite graphs
Charles Bordenave
We study the regularity of spectral measures of self-adjoint operators on infinite weighted graphs in the unimodular setting. This framework encompasses operators in the group alge…
Quadratic differentials and random walks on the dual graph of a pants decomposition
Charles Bordenave, Xinlong Dong, Dragomir Šarić
Let X be an infinite Riemann surface with an upper-bounded geodesic pants decomposition. The vertices of the corresponding dual graph G are pairs of pants and edges are cuffs with…
Quantum mixing on large Schreier graphs
Charles Bordenave, Cyril Letrouit, Mostafa Sabri
We prove quantum ergodicity and quantum mixing for sequences of finite Schreier graphs converging to an infinite Cayley graph whose adjacency operator has absolutely continuous spe…
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…
Freeness for tensors
Remi Bonnin, Charles Bordenave
We pursue the current developments in random tensor theory by laying the foundations of a free probability theory for tensors and establish its relevance in the study of random ten…