  Recent experiments have emphasized that our understanding of the interplay of
electron correlations and randomness in solids is still incomplete. We address
this important issue and demonstrate that particle-hole (ph) symmetry plays a
crucial role in determining the effects of disorder on the transport and
thermodynamic properties of the half-filled Hubbard Hamiltonian. We show that
the low-temperature conductivity decreases with increasing disorder when
ph-symmetry is preserved, and shows the opposite behavior, i.e. conductivity
increases with increasing disorder, when ph-symmetry is broken. The Mott
insulating gap is insensitive to weak disorder when there is ph-symmetry,
whereas in its absence the gap diminishes with increasing disorder.
