Self-interacting random walks are endowed with long-range memory effects that emerge
from the interaction of the random walker at time t with the territory that it has visited at earlier
times t′< t. This class of non-Markovian random walks has applications in a broad range of
examples, from insects to living cells, where a random walker locally modifies its
environment—leaving behind footprints along its path and, in turn, responding to its own
footprints. Because of their inherent non-Markovian nature, the exploration properties of self …

Self-interacting random walks are endowed with long range memory effects that emerge
from the interaction of the random walker at time $ t $ with the territory that it has visited at
earlier times $ t'< t $. This class of non Markovian random walks has applications in a broad
range of examples, ranging from insects to living cells, where a random walker modifies
locally its environment--leaving behind footprints along its path, and in turn responds to its
own footprints. Because of their inherent non Markovian nature, the exploration properties of …