Tiger and Rabbits: a single trap and many random walkers

We study a one-dimensional system with a single trap (Tiger) initially located at the origin, and many random-walkers (Rabbits) initially uniformly distributed throughout the infinite or the semi-infinite space. For a mobile imperfect trap, we study the spatiotemporal properties of the system, such as the trapping rate, the particle distribution and the segregation around the trap, all as a function of the diffusivities of both the trap and the walkers. For a static trap, we present results of various measures of segregation, in particular on a few types of disordered chains, such as random local bias fields (the Sinai model) and random transition rates.