Year: 2013
Type: article
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 non-Gaussian density fields.
DOI: 10.1093/mnras/stt987
Authors: Arya Farahi, Andrew J. Benson
Institutions: University of Michigan, Carnegie Observatories
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1964746525