Random walkers on a deformable medium

We consider random walkers that deform the medium as they move, enabling a faster motion in regions which have been recently visited. This induces an effective attraction between mediated by medium, can be regarded space metric, giving rise to statistical mechanics toy model either for gravity, through deformable matter or adaptable geometry. In strong-deformability regime, we find diffusion is initially described porous equation, thus yielding subdiffusive behavior of localized cloud particles. Indeed, while average width single will sustain $\sigma\sim t^{1/2}$ growth, combined whole ensemble grow like t^{1/3}$ certain time regime. difference accounted strong correlations particles, explore indirectly fluctuations center mass and expected value experienced density, defined density measured particles themselves.