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How do I select a set of uniformly random points from some finite portion of the upper half plane model $$\mathbb{H}= \{ (x ,y) \mid y > 0; x, y \in \mathbb{R} \}$$ with the usual hyperbolic metric? Usually, in flat space, I can select $x,y$ uniformly at random, but now I need a non-uniform densi...
In mathematics, stochastic geometry is the study of random spatial patterns. At the heart of the subject lies the study of random point patterns. This leads to the theory of spatial point processes, hence notions of Palm conditioning, which extend to the more abstract setting of random measures.
== Models ==
There are various models for point processes, typically based on but going beyond the classic homogeneous Poisson point process (the basic model for complete spatial randomness) to find expressive models which allow effective statistical methods.
The point pattern theory provides a m...
