Friday, May 31, 2013

1305.6987 (Jeffrey Schenker)

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

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