One step beyond: the excursion set approach with correlated steps

2012/01/18 by Marcello Musso, Ravi K. Sheth · 7 citations
Agricultural and Biological Sciences · Environmental Science · Mathematics · Physics and Astronomy · #Ecology and Vegetation Dynamics Studies #Plant and animal studies #Stochastic processes and statistical mechanics #astro-ph.CO #hep-th

paper · pdf · doi:10.1111/j.1745-3933.2012.01266.x

published as Mon. Not. Roy. Astron. Soc. Lett. 423 (2012) L102 - L106 · 5 pages, 1 figure. Uses mn2e class style

arxiv created 2012/01/18 · openalex publication_date 2012/04/25 · arxiv updated 2013/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

ABSTRACT We provide a simple formula that accurately approximates the first crossing distribution of barriers having a wide variety of shapes, by random walks with a wide range of correlations between steps. Special cases of it are useful for estimating halo abundances, evolution and bias, as well as the non-linear counts in cells distribution. We discuss how it can be extended to allow for the dependence of the barrier on quantities other than overdensity, to construct an excursion set model for peaks, and to show why assembly and scale-dependent bias are generic even at the linear level.

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• Cosmology with galaxy clusters: Systematic effects in the halo mass function
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• Bias deconstructed: unravelling the scale dependence of halo bias using real-space measurements
• Mass accretion rates and multi-scale halo environment in cold and warm dark matter cosmologies
• Effective window function for Lagrangian halos
• A Stochastic Theory of the Hierarchical Clustering. I. Halo Mass Function

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