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On Random Walks with a General Moving Barrier

Jun Zhang·Lam Hui
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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 an 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 which can be remedied using the method described here.

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Jun Zhang, Lam Hui. 2005-08-17. On Random Walks with a General Moving Barrier. https://doi.org/10.1086/499802

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