7 papers
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…
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 Å ariÄ
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…
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…
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…