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The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source, part I
largest eigenvalue of real symmetric Hermitian and Hermitian self-dual random matrix rank one external source
2011/2/22
We consider the limiting location and limiting distribution of the largest eigenvalue in real
symmetric (β = 1), Hermitian (β = 2), and Hermitian self-dual (β = 4) random matrix models
with rank 1 e...
Products of Independent Non-Hermitian Random Matrices
Products Independent Non-Hermitian Random Matrices
2011/2/24
For fixed m > 1, we consider m independent n×n non-Hermitian random matrices X1, . . . ,Xm with i.i.d. centered entries with a finite (2 + )-th moment, > 0. As n tends to infinity, we show that the...
Spectra of random Hermitian matrices with a small-rank external source: supercritical and subcritical regimes
Spectra of random Hermitian matrices small-rank external source: supercritical subcritical regimes
2010/12/9
Random Hermitian matrices with a source term arise, for instance, in the study of non-ntersecting Brownian walkers [1, 20] and sample covariance matrices [4]. We consider the case when the n × n exter...