Article

# Eigenvalue Statistics for Lattice Hamiltonian with Off-diagonal Disorder

Journal of Statistical Physics (impact factor: 1.4). 04/2012; 143(3):509-522. DOI:10.1007/s10955-011-0190-2

ABSTRACT This short note deals with a certain kind of lattice Hamiltonian with off-diagonal disorder. Based on the exponential decay
of the fractional moment of the Green function, we are able to prove that the properly rescaled eigenvalues of the random
Hamiltonian are distributed as a Poisson point process with intensity measure given by the density of states. One of the key
step in this proof is the Minami-type estimate. As a crucial ingredient, we also use the Minami-type estimate to study some
important properties of the random Hamiltonian, such as multiplicity of the eigenvalues and quantitative estimate of the localization
centers.

KeywordsOff-diagonal disorder–Localization–Eigenvalue statistics–Minami-type estimates

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### Keywords

eigenvalues

exponential decay

fractional moment

Green function

KeywordsOff-diagonal disorder–Localization–Eigenvalue statistics–Minami-type estimates

lattice Hamiltonian

Minami-type estimate

Poisson point process

quantitative estimate

random Hamiltonian

rescaled eigenvalues

short note deals

states