Edge universality for deformed Wigner matrices
Lee, Jioon
Schnelli, Kevin
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.
World Scientific Publishing
2015
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://research-explorer.ista.ac.at/record/1674
Lee J, Schnelli K. Edge universality for deformed Wigner matrices. <i>Reviews in Mathematical Physics</i>. 2015;27(8). doi:<a href="https://doi.org/10.1142/S0129055X1550018X">10.1142/S0129055X1550018X</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1142/S0129055X1550018X
info:eu-repo/semantics/openAccess