Statistical geometry and lattices

Statistical geometry furnishes the tool that allows the transfer of results from a lattice with finite lattice parameter to the continuum. Since latti ce simulations are simpler than continuum ones, this suggests that larger s cale simulations for the continuum might be more effectively carried out on a lattice with finite lattice parameter followed by the indicated transfer . We also show that a statistical geometry, peculiar to hard particles on a lattice, can be developed. Among other things, this opens the possibility that a scaled particle theory on a lattice might be derived.