A causal set point sampler for, in principle, arbitrary metrics
Obtain causal set point sprinking using rejection sampling for arbitrary metrics. Currently the notebook 'causal_set_tester' has an example with schwarchild.
Given the determinant of the metric
- 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. - Find the global maximum of
$c=p(x^{\mu}) + \epsilon_p$ using an optimization library - Perform rejection sampling using
$c$
- Cubature package
- Optim.jl