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Random matrices: Universality of local spectral statistics of non-Hermitian matrices
Random matrices non-Hermitian matrices Probability
2012/6/30
It is a classical result of Ginibre that the normalized bulk $k$-point correlation functions of a complex $n \times n$ gaussian matrix with independent entries of mean zero and unit variance are asymp...
Spectral Statistics of "Cellular" Billiards
Chaotic Dynamics(nlin.CD) Mathematical Physics(math-ph) Spectral Theory(math.SP)
2010/11/10
For a bounded planar domain $\Omega^0$ whose boundary contains a number of flat pieces $\Gamma_i$ we consider a family of non-symmetric billiards $\Omega$ constructed by patching several copies of $\O...
Spectral statistics for random Schrödinger operators in the localized regime
Spectral statistics random Schrö dinger operators the localized regime
2010/11/15
We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy $E$ in the localized phase. Assume ...