Stochastic geometry

This leads to the theory of spatial point processes, hence notions of Palm conditioning, which extend to the more abstract setting of random measures.

There arise questions of inference (for example, estimate the set which encloses a given point pattern) and theories of generalizations of means etc.

Connections are now being made between this latter work and recent developments in geometric mathematical analysis concerning general metric spaces and their geometry.

It is often the case that calculations are best carried out in terms of bundles of lines hitting various test-sets, rather than by working in representation space.

A notable recent result[2] proves that the cell at the origin of the Poisson line tessellation is approximately circular when conditioned to be large.

Most recently determinantal and permanental point processes (connected to random matrix theory) are beginning to play a role.