Random walks in logarithmic and power-law potentials, nonuniversal persistence, and vortex dynamics in the two-dimensional XY model

@article{Bray2000RandomWI,
title={Random walks in logarithmic and power-law potentials, nonuniversal persistence, and vortex dynamics in the two-dimensional XY model},
author={Bray},
journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
year={2000},
volume={62 1 Pt A},
pages={103-12}
}

The Langevin equation for a particle ("random walker") moving in d-dimensional space under an attractive central force and driven by a Gaussian white noise is considered for the case of a power-law force, F(r) approximately -r(-sigma). The "persistence probability," P0(t), that the particle has not visited the origin up to time t is calculated for a number of cases. For sigma>1, the force is asymptotically irrelevant (with respect to the noise), and the asymptotics of P0(t) are those of a free… CONTINUE READING