Anderson Localization for the Almost Mathieu Operator in Exponential Regime
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abstract
For the almost Mathieu operator $(H_{lambda,alpha, heta}u)_n=u_{n+1}+u_{n-1}+2lambda cos2pi( heta+nalpha)u_n$, Avila and Jitomirskaya guess that for a.e. $ heta$, $H_{lambda,alpha, heta}$ satisfies Anderson localization if $ |lambda| > e^{ \beta} $, and they establish this for $ |lambda| > e^{frac{16}{9} \beta}$. In the present paper, we extend their result to regime $ |lambda| > e^{frac{3}{2} \beta}$.
