1. Introduction & Purposes

This is a mini course that aims at an audience of advanced undergraduate and graduate students

as well as to researchers in probability, analysis and beyond. We will start with the robust method of the Lindeberg principle, which was originally used to prove the standard central limit theorem. We will then lift the Lindeberg principle to a setting of more complicated random objects such as multilinear polynomials and Wiener chaoses. The latter are intimately connected with recent developments in Stochastic PDEs and disordered systems and we will demonstrate how the Lindeberg principle can be used to obtain scaling limits of such models. We will then to move into nonlinear settings where chaos expansions are replaced by tree structures via the so called Butcher series. Relations to singular SPDEs will also be discussed.

2. Prerequisites

Introduction to Probability Theory 

3. Registration

https://reurl.cc/46xqY3