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One step beyond: The excursion set approach with correlated steps
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One step beyond: The excursion set approach with correlated steps
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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 nonlinear 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.
Forward citations
Cited by 1 Pith paper
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Large deviations for halos and voids: beyond perturbative non-gaussianities
Excursion-set halo and void abundances are derived for exponential-tailed non-Gaussian fluctuations, giving new first-passage-time formulas and a void-size-function series.
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