The effective potential of an M-matrix

  title={The effective potential of an M-matrix},
  author={Marcel Filoche and Svitlana Mayboroda and Terence Tao},
  journal={Journal of Mathematical Physics},
In the presence of a confining potential V, the eigenfunctions of a continuous Schrodinger operator −Δ + V decay exponentially with the rate governed by the part of V, which is above the corresponding eigenvalue; this can be quantified by a method of Agmon. Analogous localization properties can also be established for the eigenvectors of a discrete Schrodinger matrix. This note shows, perhaps surprisingly, that one can replace a discrete Schrodinger matrix by any real symmetric Z-matrix and… 
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