  Using Hartree-Fock orbitals with residual Coulomb repulsion, we study
spinless fermions in a two dimensional random potential. When we increase the
system size $L$ at fixed particle density, the size dependence of the average
inverse compressibility exhibits a smooth crossover from a $1/L^2$ towards a
1/L decay when the Coulomb energy to Fermi energy ratio $r_s$ increases from 0
to 3. In contrast, the distribution of the first energy excitation displays a
sharp Poisson-Wigner-like transition at $r_s \approx 1$.
