Stein’s method and stochastic geometry

September 18-20, 2024
Institute of Mathematics
Hamburg University of Technology
Hamburg, Germany


Schedule and registration

The workshop will start in the afternoon on September 18 and end at noon on September 20. It will take place at Hamburg University of Technology. Registration is free but mandatory. The organisers provide accommodation for the invited speakers and a limited number of other participants (members of SPP 2265 and junior scientists). Please register in that case not later than June 30, 2024.

Description

Stein’s method, as pioneered in the seminal work of Charles Stein, is a powerful tool to study the accuracy of the central limit theorem and, more generally, distributional approximations. On the other hand, stochastic geometry is a field of probability that aims to describe the behaviour of random geometric structures such as random spatial graphs and networks, random sets, and random tessellations, to name a few. In the last decades, there were many remarkable achievements towards combining the techniques from the two seemingly different areas to prove limit theorems and study asymptotic properties of various random geometric objects. Many such random objects are constructed from Poisson processes, whose functionals can be studied elegantly using the Malliavin-Stein method. A particular strength of Stein's method is its ability to cope with sums of dependent random variables. Such random variables naturally arise in problems from stochastic geometry due to spatial dependencies. A fruitful approach to deal with spatial dependencies is the concept of stabilisation, which was extended in several directions in recent years. The goal of this workshop is to bring together prominent researchers from Stein's method and stochastic geometry, young and senior, from Germany and outside, to exchange recent developments in the two areas and foster new collaborations.

$$ f'(x) - x f(x) = h(x) - \mathbb{E}[h(N)] $$