Abstract:

These series will start from the classical Lindeberg approach to the central limit theorem. We will then move on to see how the Lindeberg principle can be used to construct scaling limits of models of statistical mechanics, which can be expressed in the form of series of iterated Wiener integrals, also known as Wiener chaos. In this spirit and having certain applications from polymer models in mind, we will also discuss the celebrated Fourth Moment Theorem of Nualart and Peccati, which states that a sequence of random multilinear polynomials converges to a standard normal if and only if their fourth moment converges to three.