Stochastic Geometry

The thirteenth general mathematical framework is that of stochastic geometry, a branch of mathematics whose name first appeared in the 1960s. Stochastic geometry deals with the application of concepts and tools from probability theory to geometry, generally Euclidean geometry. It focuses on the study of the spatial distributions of random geometric objects (for example, in dimensions less than or equal to 3: points, curves, surfaces, or solids). From a geometric perspective, stochastic geometry is the successor to geometric probability, where random events are no longer “counted” but “measured.” It relies heavily on convex geometry, integral geometry, and geometric measure theory. Spatial point process theory is also fundamental.

Stochastic geometry is based primarily on two general concepts: random sets and random measures. Stochastic geometry is closely related...