One step beyond: The excursion set approach with correlated steps

TL;DR

This paper introduces a simple, accurate formula for the first crossing distribution in correlated random walks, enhancing models of halo formation, bias, and nonlinear counts in cosmology.

Contribution

It presents a new approximation for the first crossing distribution that accounts for correlated steps and various barrier shapes, extending excursion set theory applications.

Findings

Accurately approximates first crossing distributions for diverse barrier shapes.

Applicable to halo abundance, evolution, and bias estimations.

Shows the generic nature of assembly and scale-dependent bias.

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 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.