  The variation of single-particle spectral functions with doping is studied
numerically within the t-J model. It is shown that corresponding self energies
change from local ones at the intermediate doping to strongly nonlocal ones for
a weakly doped antiferromagnet. The nonlocality shows up most clearly in the
pseudogap emerging in the density of states, due to the onset of short-range
antiferromagnetic correlations.
