Random walks with memory are ubiquitous in nature, for example in turbulence, active matter, animal movement and finance. Generally speaking, the memory can be either persistent, such that the moving object prefers to continue moving in the same direction, or anti-persistent motion such that it prefers to backtrack.

The effects of persistence, and history-dependent motion in general, on the behavior of a single random walker are well known and have been thoroughly investigated. Also, in the vast majority of many-body systems with or without memory, increasing the number density of the moving objects decreases their mobility, expressed for example in their mean square displacement (MSD) or in the current they generate.

In this talk I will demonstrate how anti-persistent random walkers in a crowded environment behave differently, by considering a simple model of interacting particles on a lattice. In particular, I will show that the MSD of anti-persistent random walkers is non-monotonic with respect to the density, and that the bulk diffusion coefficient of the system increases with the density.