  Exploration and trapping properties of random walkers that may evanesce at
any time as they walk have seen very little treatment in the literature, and
yet a finite lifetime is a frequent occurrence, and its effects on a number of
random walk properties may be profound. For instance, whereas the average
number of distinct sites visited by an immortal walker grows with time without
bound, that of a mortal walker may, depending on dimensionality and rate of
evanescence, remain finite or keep growing with the passage of time. This
number can in turn be used to calculate other classic quantities such as the
survival probability of a target surrounded by diffusing traps. If the traps
are immortal, the survival probability will vanish with increasing time.
However, if the traps are evanescent, the target may be spared a certain death.
We analytically calculate a number of basic and broadly used quantities for
evanescent random walkers.
