3 papers
math.PR2026
Precise Delocalisation and Gumbel Laws for Eigenvectors of Wigner Matrices
Mohammed Osman
We prove a delocalisation bound for eigenvectors of Wigner matrices with the precise relationship between the size of the largest entry and the decay exponent of the probability. W…
math.PR2024
Universality for Diagonal Eigenvector Overlaps of non-Hermitian Random Matrices
Mohammed Osman
We prove the universality of the joint distribution of an eigenvalue and the corresponding diagonal eigenvector overlap, in the bulk and at the edge, for eigenvalues of complex mat…
math.PR2024
Least Non-Zero Singular Value and the Distribution of Eigenvectors of non-Hermitian Random Matrices
Mohammed Osman
We obtain a tail bound for the least non-zero singular value of when is a random matrix and is an eigenvalue of in a neighbourhood of a given point in the b…