Year: 2006
Type: article
Abstract: Random walks with a general, nonlinear barrier have found recent applications ranging from reionization topology to refinements in the excursion set theory of halos. Here we derive the first-crossing distribution of random walks with a moving barrier of arbitrary shape. Such a distribution is shown to satisfy an integral equation that can be solved by a simple matrix inversion, without the need for Monte Carlo simulations, making this useful for exploring a large parameter space. We discuss examples in which common analytic approximations fail, a failure that can be remedied using the method described here.
Source: The Astrophysical Journal
DOI: 10.1086/499802
Authors: Jun Zhang, Lam Hui
Institution: Columbia University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2032025819