Local law for eigenvalues of random Hermitian matrices with external source

Linh Tran

Local law for eigenvalues of random Hermitian matrices with external source

Probability 2013-10-22 v2

Authors: Linh Tran

Abstract

We prove a local law for eigenvalues of the random Hermitian matrices with external source $W_n=\frac{1}{n}X_n+A_n$ where $X_n$ is Wigner matrix and $A_n$ is diagonal matrix with only two values $a, -a$ on the diagonal. The local law is an essential step to prove the universality conjecture for this random matrix model.

Keywords

random matrix theory local-global principles

Cite

@article{arxiv.1310.4611,
  title  = {Local law for eigenvalues of random Hermitian matrices with external source},
  author = {Linh Tran},
  journal= {arXiv preprint arXiv:1310.4611},
  year   = {2013}
}

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