CLTs for Poisson Functionals - The Malliavin-Stein Approach
Tara Trauthwein, University of Oxford
Abstract: In this talk, we will study examples of random graphs which do not behave quite as nicely as you would want them to. When those graphs are large, quantities like the sum of all edge lengths will behave almost like a Gaussian, but a fair bit of work is needed to prove this. We will go over the basics of the Malliavin-Stein method, a superbly useful tool for the derivation of bounds on the distance between a function of a Poisson process (not necessarily related to graphs - this can be much more general) and a standard Gaussian. We will see why some quantities and some graphs present difficulties and how to tweak the method to allow for those misbehaving cases. This is based on the preprint (Trauthwein 2022).
