Spectral statistic for decaying random potentials

2014/03/13 by Dhriti Ranjan Dolai, Dolai, Dhriti Ranjan
Mathematics · #FOS: Mathematics #Random Matrices and Applications #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1403.3194

openalex publication_date 2014/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider Anderson model H^ω=-Δ+V^ω on ℓ²(ℤ^d) with decaying random potential. We study the point process ξ^ω_L,λ associated with eigenvalues of H^ω_ΛL, the retriction of H^ω to the finite cube Λ_L. Our result is that the weak limit points of \ξ^ω_L,λ\ are poisson point processes as L→∞.

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