Edge universality for deformed Wigner matrices
By Ji Oon Lee, Kevin Schnelli. 2014
79 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/a6e421be19b5e708af444df1c7ad9207af77f161
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In Discrete Mathematics and Combinatorics
In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- A Dynamical Approach to Random Matrix Theory (2017, background): “The corresponding local law was proved in [93] followed by the proof of bulk universality in [96] and the edge universality [95,96].”
- The spectral norm of random inner-product kernel matrices (2015, background): “When W is GUE and V has no spike eigenvalues, the results of [16, 41] imply that the eigenvalues of W + V stick to the limiting support, and the fluctuations of the eigenvalues at the edges of the support are also understood in various settings [48, 17, 39].”
- Anisotropic local laws for random matrices (2014, unknown): “21450 [26] Lee, JO; Schnelli, K, Edge universality for deformed Wigner matrices, Rev.”