Decorrelation estimates for random Schrödinger operators with non rank one perturbations
References
2,908 citations
"Decorrelation estimates for random ..." refers methods in this paper
...For information on Lévy processes, we refer to the books by Applebaum [2]...
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...For information on Lévy processes, we refer to the books by Applebaum [2] and by Bertoin [3]....
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...[2] D. Applebaum, Lévy processes and stochastic calculus, Cambridge Studies in Advanced Mathematics 116, second edition, Cambridge: Cambridge University Press, 2009....
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280 citations
"Decorrelation estimates for random ..." refers methods in this paper
...Poisson process by Minami [15] (see also Molchanov [16] for a model on R and Germinet-Klopp [6] for a comprehensive discussion and additional results)....
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231 citations
"Decorrelation estimates for random ..." refers background in this paper
...We say that the local Hamiltonian Hω,l satisfies (Loc) in an interval I ⊂ Σ if (1) The finite-volume fractional moment criteria of [1] holds on the interval I for some constant C > 0 sufficiently large; (2) There exists ν > 0 such that, for any p > 0, there exists q > 0 and a length scale l0 > 0 such that, for all l > l0, the following hold with probability greater than 1− Lp: (a) If φj(ω) is a normalized eigenvector of Hω,l with eigenvalue El j(ω) ∈ I, and (b) xj(ω) is a maximum of x→ |φ l j(ω)| in Λl, then, for n ∈ Λl, one has |φj(ω)(x)| 6 l e l j....
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230 citations
159 citations
"Decorrelation estimates for random ..." refers methods in this paper
...MR1509883 [8] A. Klein, S. Molchanov, Simplicity of eigenvalues in the Anderson model, J. Stat....
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...When the projectors Pi are rank one projectors, the local eigenvalue statistics in the localization regime has been proved to be given by a Poisson process by Minami [15] (see also Molchanov [16] for a model on R and Germinet-Klopp [6] for a comprehensive discussion and additional results)....
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...Bounds on eigenvalue multiplicity The extended Minami estimate may be used with the Klein-Molchanov argument [8] to bound the multiplicity of eigenvalues in the localization regime....
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...The proof of this fact follows the argument of Klein and Molchanov [8]....
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...Poisson process by Minami [15] (see also Molchanov [16] for a model on R and Germinet-Klopp [6] for a comprehensive discussion and additional results)....
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