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Analyticity of the density of states and replica method for random Schrödinger operators on a lattice. (English) Zbl 0591.60060
Summary: We analyze the density of states and some aspects of the replica method for Anderson’s tight binding model on a lattice of arbitrary dimension, with diagonal disorder. We give heuristic arguments for the conjectures that the classical value of the exponent v of the localization length is 1/2 and that the upper critical dimension, \(d_ c^{loc}\), is bounded by \(4\leq d_ c^{loc}\leq 6\).

60H25 Random operators and equations (aspects of stochastic analysis)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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