  Using quantum Monte Carlo simulations, we show that the one-dimensional
fermionic Hubbard model in a harmonic potential displays quantum critical
behavior at the boundaries of a Mott-insulating region. A local compressibility
defined to characterize the Mott-insulating phase has a non-trivial critical
exponent. Both the local compressibility and the variance of the local density
show universality with respect to the confining potential. We determine a
generic phase diagram, that allows the prediction of the phases to be observed
in experiments with ultracold fermionic atoms trapped on optical lattices.
