110 research outputs found
A strong operator topology adiabatic theorem
We prove an adiabatic theorem for the evolution of spectral data under a weak
additive perturbation in the context of a system without an intrinsic time
scale. For continuous functions of the unperturbed Hamiltonian the convergence
is in norm while for a larger class functions, including the spectral
projections associated to embedded eigenvalues, the convergence is in the
strong operator topology.Comment: 15 pages, no figure
Gaussian fluctuations for random matrices with correlated entries
For random matrix ensembles with non-gaussian matrix elements that may
exhibit some correlations, it is shown that centered traces of polynomials in
the matrix converge in distribution to a Gaussian process whose covariance
matrix is diagonal in the basis of Chebyshev polynomials. The proof is
combinatorial and adapts Wigner's argument showing the convergence of the
density of states to the semicircle law
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