Geometric Functionals of Polyconvex Excursion Sets of Poisson Shot Noise Processes

Explore the geometric properties of Poisson shot noise processes in this 21-minute lecture from the Hausdorff Center for Mathematics. Delve into the analysis of excursion sets within compact convex observation windows, focusing on polyconvex cases that include the Boolean model. Examine the behavior of geometric functionals, particularly intrinsic volumes, as observation windows grow. Investigate the asymptotics of expectation and variance, discover a lower variance bound, and learn about the central limit theorem applied to these processes. Gain insights into this specialized area of mathematical research and its implications for understanding random sets.