  We study the ground state, sum a_X |X>, of N hard-core bosons on a finite
lattice in configuration space, X={x_1,...,x_N}. All a_X being positive, the
ratios a_X / sum a_Y can be interpreted as probabilities P_a (X). Let E denote
the energy of the ground state and B_X the number of nearest-neighbor
particle-hole pairs in the configuration X. We prove the concentration of P_a
to X's with B_X in a sqrt(|E|)-neighborhood of |E|, show that the average of
a_X over configurations with B_X=n increases exponentially with n, discuss
fluctuations about this average, derive upper and lower bounds on E and give an
argument for off-diagonal long-range order in the ground state.
