# Brownian flights over a circle – Archive ouverte HAL

### Alexander VladimirovSenya ShlosmanSergei Nechaev 1

#### Alexander Vladimirov, Senya Shlosman, Sergei Nechaev. Brownian flights over a circle. Physical Review E , American Physical Society (APS), 2020, 102 (1), ⟨10.1103/PhysRevE.102.012124⟩. ⟨hal-03009773⟩

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 $R$.

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques