/causal-set-sampler

A causal set point sampler for arbitrary metrics

Primary LanguageMathematicaMIT LicenseMIT

causal-set-sampler

A causal set point sampler for, in principle, arbitrary metrics

Description

Obtain causal set point sprinking using rejection sampling for arbitrary metrics. Currently the notebook 'causal_set_tester' has an example with schwarchild.

Methodology

Given the determinant of the metric $\sqrt{-g}$, a coordinate bound, and the sprinkling density $\rho$ we do the following:

  1. Integrate $\sqrt{-g}$ over the domain to obtain the coordinate sampling distribution $p(x^{\mu}) = \sqrt{-g(x^{\mu})} / \int \sqrt{-g}$, where the integration is over the provided bounds. Currently only connected regions are supported.
  2. Find the global maximum of $c=p(x^{\mu}) + \epsilon_p$ using an optimization library
  3. Perform rejection sampling using $c$

Requirements

  1. Cubature package
  2. Optim.jl