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Survival probability of a Brownian motion in a planar wedge of arbitrary angle
Marie Chupeau1, Olivier Bénichou1, Satya N Majumdar2
1Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), Université Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex, France.
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 π/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 π 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.
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