On random walks with a general moving barrier

Aug, 2005
6 pages
Published in:
  • Astrophys.J. 641 (2006) 641-646
e-Print:

Citations per year

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Abstract: (arXiv)
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.
  • cosmology: theory
  • galaxies: halos
  • galaxies: structure
  • intergalactic medium
  • large-scale structure of universe
  • methods: analytical
  • methods: numerical