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.