Classical localization problem: a survey

Abstract

We survey classical localization problems arising from quantum network models in symmetry class C and their mappings to history-dependent random walks on directed lattices. We describe how localization versus delocalization of trajectories can be analysed using percolation methods and combinatorial enumeration of path intersection patterns. In particular, we review results establishing almost sure finiteness of trajectories for parameters near criticality and polynomial bounds on the confinement length in cylindrical geometries.