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The Excursion set approach: Stratonovich approximation and Cholesky decomposition

Nikakhtar, F ; Sharif University of Technology | 2018

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  1. Type of Document: Article
  2. DOI: 10.1093/mnras/sty1415
  3. Publisher: Oxford University Press , 2018
  4. Abstract:
  5. The excursion set approach is a framework for estimating how the number density of nonlinear structures in the cosmic web depends on the expansion history of the universe and the nature of gravity. A key part of the approach is the estimation of the first-crossing distribution of a suitably chosen barrier by random walks having correlated steps: The shape of the barrier is determined by the physics of non-linear collapse, and the correlations between steps by the nature of the initial density fluctuation field. We describe analytic and numerical methods for calculating such first up-crossing distributions. While the exact solution can be written formally as an infinite series, we show how to approximate it efficiently using the Stratonovich approximation. We demonstrate its accuracy using Monte Carlo realizations of the walks, which we generate using a novel Cholesky-decomposition based algorithm, which is significantly faster than the algorithm that is currently in the literature. © 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society
  6. Keywords:
  7. Cosmology theory ; Dark matter ; Galaxies: haloes ; Methods: numerical
  8. Source: Monthly Notices of the Royal Astronomical Society ; Volume 478, Issue 4 , 2018 , Pages 5296-5300 ; 00358711 (ISSN)
  9. URL: https://academic.oup.com/mnras/article/478/4/5296/5025661