Random Processes in Random Environments

Lead CI: Dirk Kroese

Random walks in random environments (RWREs) are well-known models for motion in disordered media, such as transport of water through porous rocks or charge transport in semiconducting materials.

The theoretical behaviour of multi-dimensional RWREs is poorly understood, both from a theoretical and computational point of view. Even for 1-dimensional random walks the evaluation of various system characteristics such as the drift of the random walk has received little attention. The goal of this proposal is to significantly advance the state of the art for RWREs by analysing the behaviour of the general class of quasi-birth-and-death (QBD) processes in multi-dimensional random environments. Such processes are natural generalizations of 1-dimensional RWREs and it is expected that their analysis would bear resemblance to 1-dimensional case, which is well understood.