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
 

Dong Miao