no code implementations • 11 Mar 2021 • Giorgio Cipolloni, László Erdős, Dominik Schröder
We consider the quadratic form of a general deterministic matrix on the eigenvectors of an $N\times N$ Wigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large $N$ limit.
Probability Mathematical Physics Mathematical Physics 60B20, 15B52
no code implementations • 19 Feb 2021 • Giorgio Cipolloni, László Erdős, Dominik Schröder
We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices $W$ and provide an optimal error bound on their fluctuation with very high probability.
Probability Mathematical Physics Functional Analysis Mathematical Physics Operator Algebras 60B20, 15B52, 46L54
no code implementations • 24 Dec 2020 • Giorgio Cipolloni, László Erdős, Dominik Schröder
We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension.
Probability Mathematical Physics Mathematical Physics 60B20, 15B52, 58J51, 81Q50
no code implementations • 24 Dec 2020 • Giorgio Cipolloni, László Erdős, Dominik Schröder
We consider the fluctuations of regular functions $f$ of a Wigner matrix $W$ viewed as an entire matrix $f(W)$.
Probability Mathematical Physics Mathematical Physics 60B20, 15B52
