Survival probability of a Brownian motion in a planar wedge of arbitrary angle

Abstract

We study the survival probability and the first-passage time distribution for a Brownian motion in a planar wedge with infinite absorbing edges. We generalize existing results obtained for wedge angles of the form $\pi /n$ with $n$ a positive integer to arbitrary angles, which in particular cover the case of obtuse angles. We give explicit and simple expressions of the survival probability and the first-passage time distribution in which the difference between an arbitrary angle and a submultiple of $\pi$ is contained in three additional terms. As an application, we obtain the short time development of the survival probability in a wedge of arbitrary angle.

References in corpus (2)

• First-passage times in complex scale-invariant media
• Persistence and First-Passage Properties in Non-equilibrium Systems

Cited by in corpus (12)

• The convex hull of the run-and-tumble particle in a plane
• Learning physical properties of anomalous random walks using graph neural networks
• First-encounter time of two diffusing particles in confinement
• Statistics of fermions in a $d$-dimensional box near a hard wall
• Mean exit time for diffusion on irregular domains
• Mean perimeter of the convex hull of a random walk in a semi-infinite medium
• Fluctuation Exponents of the KPZ equation on a large torus
• On sequences of records generated by planar random walks
• First-passage times to a fractal boundary: local persistence exponent and its log-periodic oscillations
• Simulation of Reflected Brownian motion on two dimensional wedges
• Mean exit time in irregularly-shaped annular and composite disc domains
• Diffusion in a fluid flow generated by a source at the apex of a wedge