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arXiv · 1305.6987

How large is large? Estimating the critical disorder for the Anderson model

Jeffrey Schenker
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Abstract

Complete localization is shown to hold for the $d$-dimensional Anderson model with uniformly distributed random potentials provided the disorder strength $λ>λ_{And}$ where $λ_{\text{And}}$ satisfies $λ_{\text{And}}=μ_d e \ln λ_{\text{And}}$ with $μ_d$ the self-avoiding walk connective constant for the lattice $\mathbb{Z}^d$. Notably $λ_{\text{And}}$ is precisely the large disorder threshold proposed by Anderson in 1958.

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Jeffrey Schenker. 2014-10-17. How large is large? Estimating the critical disorder for the Anderson model. https://doi.org/10.1007/s11005-014-0729-7

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