Brownian flights over a circle

Abstract

The stationary radial distribution, $P(\rho )$, of the random walk with the diffusion coefficient $D$, which winds with the tangential velocity $V$ around the impenetrable disc of radius $R$ for $R\gg 1$ 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 the constant which depends on the parameters $D$ and $V$ and is independent on $R$.

arXiv comment7 pages, 1 figure

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• Lifshitz tails at spectral edge and holography with a finite cutoff
• Non-algebraic first return probability of a stretched random walk near a convex boundary and its effect on adsorption