Brownian flights over a circle.

ABSTRACT

The stationary radial distribution, P(ρ), of a random walk with the diffusion coefficient D, which winds at the tangential velocity V around an impenetrable disk of radius R for R≫D/V converges to the distribution involving the Airy function. Typical trajectories are localized in the circular strip [R,R+δR^{1/3}], where δ is a constant which depends on the parameters D and V and is independent of R.