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 $R$.

7 pages, 1 figure

References in corpus (4)

• Growing interfaces uncover universal fluctuations behind scale invariance
• Constrained Brownian motion: Fluctuations away from circular and parabolic barriers
• The Airy distribution: experiment, large deviations and additional statistics
• Bethe Ansatz in the Bernoulli Matching Model of Random Sequence Alignment

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