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

• Received 23 March 2020
• Accepted 22 June 2020

DOI:https://doi.org/10.1103/PhysRevE.102.012124