4 papers
On the spectral radius of the ratio of Girko matrices
Djalil Chafaï, David GarcÃa-Zelada, Yuan Yuan Xu
Girko matrices have independent and identically distributed entries of mean zero and unit variance. In this note, we consider the random matrix model formed by the ratio of two ind…
Singular central limit theorems for the spherical ensemble and beyond
Djalil Chafaï, David GarcÃa-Zelada, Yuan Yuan Xu
We study the fluctuations of logarithmic Green singularities in the spherical ensemble, viewed as a random discretization of the two-sphere. Smooth observables exhibit the usual So…
On cutoff via rigidity for high dimensional curved diffusions
Djalil Chafaï, Max Fathi
We consider overdamped Langevin diffusions in Euclidean space, with curvature equal to the spectral gap. This includes the Ornstein-Uhlenbeck process as well as non-Gaussian and no…
On the cutoff phenomenon for fast diffusion and porous medium equations
Djalil Chafaï, Max Fathi, Nikita Simonov
The cutoff phenomenon, conceptualized at the origin for finite Markov chains, states that for a parametric family of evolution equations, started from a point, the distance towards…