Anderson-Bernoulli localization at large disorder on the 2D lattice

2020/02/26 by Linjun Li, Li, Linjun · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Probability (math.PR) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2002.11580

openalex publication_date 2020/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Anderson model at large disorder on ℤ² where the potential has a symmetric Bernoulli distribution. We prove that Anderson localization happens outside a small neighborhood of finitely many energies. These finitely many energies are Dirichlet eigenvalues of the minus Laplacian restricted on some finite subsets of ℤ².

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• Survey on Lattice Gas Models on 2D Lattices: Critical Behavior of Closed Trajectories
• Random Schrödinger operator with singular potentials

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