Kevin Schnelli

Bulk universality for deformed Wigner matrices

We consider N×N random matrices of the form H=W+V where W is a real symmetric or complex Hermitian Wigner matrix and V is a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W, and we choose V so that the eigenvalues of W and V are typically of the same order. For a large class of diagonal matrices V, we show that the local statistics in the bulk of the spectrum are universal in the limit of large N.

Tracy–Widom distribution for the largest eigenvalue of real sample covariance matrices with general population.

We consider sample covariance matrices of the form

Local deformed semicircle law and complete delocalization for Wigner matrices with random potential

\mathcal{Q}=(\Sigma^{1/2}X)(\Sigma^{1/2} X)^*

Local Law of Addition of Random Matrices on Optimal Scale

, where the sample

Universality for random matrix flows with time-dependent density

X

Edge universality for deformed Wigner matrices

is an

Local law and Tracy–Widom limit for sparse random matrices

M\times N

Local stability of the free additive convolution

random matrix whose entries are real independent random variables with variance

Convergence rate for spectral distribution of addition of random matrices

1/N

Extremal eigenvalues and eigenvectors of deformed Wigner matrices

and where