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    Article

    Extremal Theory for Spectrum of Random Discrete Schrödinger Operator. III. Localization Properties

    In this paper, we study the asymptotic localization properties with high probability of the Kth eigenfunction (associated with the Kth largest eigenvalue, K⩾1 fixed) of the multidimensional Anderson Hamiltonian i...

    A. Astrauskas in Journal of Statistical Physics (2013)

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    Article

    Extremal Theory for Spectrum of Random Discrete Schrödinger Operator. II. Distributions with Heavy Tails

    We study the asymptotic structure of the first K largest eigenvalues λ k,V and the corresponding eigenfunctions ψ(⋅;λ ...

    A. Astrauskas in Journal of Statistical Physics (2012)

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    Article

    Extremal Theory for Spectrum of Random Discrete Schrödinger Operator. I. Asymptotic Expansion Formulas

    We consider the spectral problem for the random Schrödinger operator on the multidimensional lattice torus increasing to the whole of lattice, with an i.i.d. potential (Anderson Hamiltonian). We obtain the exp...

    A. Astrauskas in Journal of Statistical Physics (2008)