Universal character of escape kinetics from finite intervals

We study a motion of an anomalous random walker on finite intervals restricted by two absorbing boundaries. The competition between anomalously long jumps and long waiting times leads to a very general kind of behavior. Trapping events distributed according to the power-law distribution result in occurrence of the Mittag–Leffler decay pattern which in turn is responsible for universal asymptotic properties of escape kinetics. The presence of long jumps which can be distributed according to non-symmetric heavy tailed distributions does not affect asymptotic properties of the survival probability. Therefore, the probability of finding a random walker within a domain of motion decays asymptotically according to the universal pattern derived from the Mittag–Leffler function, which describes decay of single modes in subdiffusive dynamics