Proposal Description

Stochastic geometry deals with questions about the large-scale behaviour of random geometric objects. These can be random graphs, polytopes, tessellations or others – the common point being that they usually arise from a random spatial point process. An example of a studied question would be the following: given a random point process, one can construct a graph according to some deterministic rule set. What are the distributions of the graph's properties when the point set is large? Do they satisfy (central) limit theorems?
Applications of stochastic geometry reach far: it is used in astronomy, telecommunications and wireless network modelling, image analysis, stereology and many other fields.
Stein’s Method has proven to be an indispensable tool for showing distributional convergence in a wide range of areas across probability and statistics. In essence, it is a technique which allows one to gauge the distance between probability distributions using characteristic expressions of the target distribution in a very convenient way. Combined with stochastic geometry, it often leads to stunningly sharp quantitative convergence results.
In recent years, the use of Stein’s Method in stochastic geometry has lead to a multitude of important advances, many of which have been brought along by the speakers of this session. The topics discussed will include the Malliavin-Stein method, stabilization theory and relations to real-life networks.
This session is of interest to the stochastic geometry community, and in a wider sense to anyone who deals with limit theorems across all subject areas, as it exhibits different ways of applying Stein’s Method in a context relevant to statistics.