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

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 . Additionally, the particle resets with a constant rate 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 arbitrary spatial dimensions. At late times, the typical displacement of ...