Seminar/ Colloquium

Title: Geometry of random fields: an integral geometric view

Abstract: Given a (smooth) random function $f:\mathbb{R}^d \to \mathbb{R}$, studying its excursion sets $f^{-1}[u,\infty)$ has a long history with motivations coming from statistical hypothesis testing, cosmology, stereology, and integral geometry, to name a few. Questions pertaining to the characterisation of excursion sets are often considered very relevant, and very challenging. For instance, one is often interested in obtaining a precise probabilistic description of the volume, surface area, perimeter of excursion sets of random fields. In this talk, we shall present an asymptotic description of (some) such geometric functionals of excursion sets of random fields in different scenarios.