**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