Hölder continuity of Lyapunov exponent for quasi-periodic Jacobi operators

Kai Tao

We consider the quasi-periodic Jacobi operator $H_{x,\omega }$ in $l^2(\mathbb{Z})$ $(H_{x,\omega }\varphi )(n)=-b(x+(n+1)\omega )\varphi (n+1)-b(x+n\omega )\varphi (n-1)+a(x+n\omega )\varphi (n)=E\varphi (n),n\in \mathbb{Z},$ where $a(…