Abstract
Let H=1/2Δ+V on l2(B), whereB is the Bethe lattice andV(x),xε B, are i.i.d.r.v.'s with common probability distributionμ. It is shown that for distributions sufficiently close to the Cauchy distribution, the density of statesρ(E) is analytic in a strip about the real axis.
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Acosta, V., Klein, A. Analyticity of the density of states in the anderson model on the Bethe lattice. J Stat Phys 69, 277–305 (1992). https://doi.org/10.1007/BF01053794
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DOI: https://doi.org/10.1007/BF01053794