## Topics in Probability: Gaussian Analysis Math 7880-1, Spring 2015 University of Utah

Time & Place: MWF 9:40-10:30 a.m. LCB 222
Instructor: Davar Khoshnevisan JWB 102

Course Synopsis. Let $\mathbb{P}_n$ denote the canonical Gaussian measure - or the standard multivariate normal - on $\mathbb{R}^n$; that is, $\mathbb{P}_n(A) := \int_A \frac{\exp\left(-\frac12\|x\|^2\right)}{(2\pi)^{n/2}}\,{\rm d}x,$ for all Borel sets $A$ in $\mathbb{R}^n$. This is an object that you have seen, say in the context of the classical central limit theorem. And some of you have studied many of the elementary properties of $\mathbb{P}_n$ in courses such as 6010 and 6020 [linear models]. In this course we study some of the deeper structure of the "Gauss space" $(\mathbb{R}^n\,,\mathcal{B}(\mathbb{R}^n)\,,\mathbb{P}_n)$. We will also see that our analysis of $\mathbb{P}_n$ yields a much better understanding of the theory of Gaussian processes [which we will introduce as well].