Exact Propagators of One-Dimensional Self-Interacting Random Walks.

Self-interacting random walks (SIRWs) show long-range memory effects that result from the interaction of the random walker at time t with the territory already visited at earlier times t^{'} View Article and Find Full Text PDF

Aging dynamics of d-dimensional locally activated random walks.

Locally activated random walks are defined as random processes, whose dynamical parameters are modified upon visits to given activation sites. Such dynamics naturally emerge in living systems as varied as immune and cancer cells interacting with spatial heterogeneities in tissues, or, at larger scales, animals encountering local resources. At the theoretical level, these random walks provide an explicit construction of strongly non-Markovian and aging dynamics.