  For a symmetric, homogeneous and irreducible random walk on d-dimensional
integer lattice Z^d, having zero mean and a finite variance of jumps, we study
the passage times (with possible infinite values) determined by the starting
point x, the hitting state y and the taboo state z. We find the probability
that these passages times are finite and analyze the tails of their cumulative
distribution functions. In particular, it turns out that for the random walk on
Z^d, except for a simple (nearest neighbor) random walk on Z, the order of the
tail decrease is specified by dimension d only. In contrast, for a simple
random walk on Z, the asymptotic properties of hitting times with taboo
essentially depend on the mutual location of the points x, y and z. These
problems originated in our recent study of branching random walk on Z^d with a
single source of branching.
