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arXiv · 2002.09965

Brownian flights over a circle

Alexander Vladimirov·Senya Shlosman·Sergei Nechaev
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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 $R$.

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Alexander Vladimirov, Senya Shlosman, Sergei Nechaev. 2020-02-23. Brownian flights over a circle. https://doi.org/10.1103/physreve.102.012124

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