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Random matrices: Universality of local spectral statistics of non-Hermitian matrices
Random matrices non-Hermitian matrices Probability
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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...
Universality of local spectral statistics of random matrices
Random matrix Local semicircle law Tracy-Widom distribution Dyson Brownian motion
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2011/7/28
Abstract: The Wigner-Gaudin-Mehta-Dyson conjecture asserts that the local eigenvalue statistics of large random matrices exhibit universal behavior depending only on the symmetry class of the matrix e...
Spectral Statistics of "Cellular" Billiards
Chaotic Dynamics(nlin.CD) Mathematical Physics(math-ph) Spectral Theory(math.SP)
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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
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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 ...