Arrival Statistics and Exploration Properties of Mortal Walkers

We study some of the salient features of the arrival statistics and explo- ration properties of mortal random walkers, that is, walkers that may die as they move, or as they wait to move. Such evanescence or death events have profound consequences for quantities such as the number of distinct sites visited which are relevant for the computation of encounter- controlled rates in chemical kinetics. We exploit the observation that well-known methods developed decades ago for immortal walkers are widely applicable to mortal walkers. The particular cases of exponential and power-law evanescence are considered in detail. Finally, we discuss the relevance of our results to the target problem with mortal traps and a particular application thereof, namely, the defect di?usion model. Evanescence of defects is postulated as a possible complementary contri- bution or perhaps even an alternative to anomalous di?usion to explain observed stretched exponential relaxation behavior.