162 citations · 1.3k across the 49 of their papers we have counts for
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Singular central limit theorems for the spherical ensemble and beyond
Djalil Chafaï, David García-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 the spectral radius of the ratio of Girko matrices
Djalil Chafaï, David García-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…
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…
Monotonicity of the logarithmic energy for random matrices
Djalil Chafaï, Benjamin Dadoun, Pierre Youssef
It is well-known that the semi-circle law, which is the limiting distribution in the Wigner theorem, is the minimizer of the logarithmic energy penalized by the second moment. A ve…
Threshold condensation to singular support for a Riesz equilibrium problem
Djalil Chafaï, Edward B. Saff, Robert S. Womersley
We compute the equilibrium measure in dimension d=s+4 associated to a Riesz s-kernel interaction with an external field given by a power of the Euclidean norm. Our study reveals th…
Aspects of Coulomb gases
Djalil Chafaï
Coulomb gases are special probability distributions, related to potential theory, that appear at many places in pure and applied mathematics and physics. In these short expository…