Ultra slow sub-logarithmic diffusion of a sluggish random walker subject to resetting with memory (opens in new tab)

arXiv:2603.01149v1 Announce Type: new Abstract: We solve a model of sluggish stochastic motion in which a Brownian particle diffuses with a diffusion coefficient that decays algebraically with the distance to the origin, as $|x|^{-\alpha}$. Additionally, the particle resets with a constant rate $r$ to positions previously visited in the past, so that frequently visited regions are more likely to be revisited. An exact expression is obtained at all times for the position distribution in arbit...