Abstract: Laplacian in an arbitrary finite domain D in Z^d. This represents the ground state energy of electrons hoppings on a lattice. Inspired by a result of Li and Yau for the analogous problem in the continuum, we prove that this sum behaves like a "bulk term", i.e. a term proportional to the volume of the domain, plus a boundary correction. This result was obtained jointly with J.K. Freericks and E.H. Lieb and is archived in math-ph/0107003