Elke Rosenberger, Markus Klein
Agmon-Type estimates for a class of difference operators
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ABSTRACT. We analyze a general class of difference operators H_epsilon =
T_epsilon + V_epsilon on
l^2(epsilon Z^d),
where V_epsilon is a one-well potential and epsilon is a small parameter.
We construct a Finslerian distance d induced by H_epsilon and show that short integral curves are
geodesics.
Then we show that Dirichlet eigenfunctions decay exponentially with a rate
controlled by the Finsler distance to the well. This is analog to semiclassical
Agmon estimates for Schr dinger operators.