10.1142/S0129055X1550018X
Lee, Jioon
Jioon
Lee
Schnelli, Kevin
Kevin
Schnelli
Edge universality for deformed Wigner matrices
World Scientific Publishing
2015
2018-12-11T11:53:24Z
2019-01-24T13:04:02Z
journal_article
https://research-explorer.app.ist.ac.at/record/1674
https://research-explorer.app.ist.ac.at/record/1674.json
We consider N × N random matrices of the form H = W + V where W is a real symmetric Wigner matrix and V 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 rescaled distribution of the extremal eigenvalues is given by the Tracy-Widom distribution F1 in the limit of large N. Our proofs also apply to the complex Hermitian setting, i.e. when W is a complex Hermitian Wigner matrix.