One step beyond: the excursion set approach with correlated steps

Authors

  • Marcello Musso,

    Corresponding author
    1. The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
    2. CP3, Université de Louvain, 2 Chemin du Cyclotron, 1348 Louvain-la-Neuve, Belgium
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  • Ravi K. Sheth

    Corresponding author
    1. The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
    2. Center for Particle Cosmology, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104, USA
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E-mail: marcello.musso@uclouvain.be (MM); sheth@ictp.it (RKS)

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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