Agmon-Type Estimates for a Class of Difference Operators

We analyze a general class of self-adjoint difference operators , where V _ε is a one-well potential and ε is a small parameter. We construct a Finslerian distance d induced by H _ε 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. Submitted: February 23, 2008. Accepted: May 23, 2008.