Excursion set theory for correlated random walks
Abstract
We present a new method to compute the first crossing distribution in excursion set theory for the case of correlated random walks. We use a combination of the path integral formalism of Maggiore & Riotto, and the integral equation solution of Zhang & Hui and Benson et al. to find a numerically and convenient algorithm to derive the first crossing distribution. We apply this methodology to the specific case of a Gaussian random density field filtered with a Gaussian smoothing function. By comparing our solutions to results from Monte Carlo calculations of the first crossing distribution we demonstrate that approximately it is in good agreement with exact solution for certain barriers, and at large masses. Our approach is quite general, and can be adapted to other smoothing functions and barrier function and also to nonGaussian density fields.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 August 2013
 DOI:
 10.1093/mnras/stt987
 arXiv:
 arXiv:1303.0337
 Bibcode:
 2013MNRAS.433.3428F
 Keywords:

 methods: analytical;
 galaxies: haloes;
 cosmology: theory;
 dark matter;
 Astrophysics  Cosmology and Extragalactic Astrophysics;
 8508;
 J.2
 EPrint:
 15 pages, 7 figures, Accepted for publication in MNRAS. Some corrections following comments from referee