Let $\mathbb T$ be an index set, usually a subset of $\mathbb R^N$ for some $N$. Then a collection of random variables $\{X_t\}_{t \in \mathbb T}$ on the same probability space $(\Omega, \mathcal H, \mathbb… Read More »Random Processes & Random Fields
Let $(E, \mathcal E)$ be a measurable space, and let $(E^N, \mathcal E^{\otimes N})$ be the product space equipped with the product $\sigma$-algebra. We will view $\mathbf x = (x_1, \ldots, x_N)$ as the position… Read More »Point Processes
Theory of Probability Winter/Spring 2023. MWF 10-11am. Catalog description: Measure and integration, probability spaces, laws of large numbers, central-limit theory, conditioning, martingales, random walks. We will cover most of Probability and Stochastics by Erhan Çinlar.… Read More »Math 672/673
In Nathan Hunter’s thesis, the inner product of two monomials $x^M$ and $x^L$, with $M \leq L$ are given as $$\begin{eqnarray}\langle x^M , x^L \rangle &=& 2 \pi \sum_{n=-NM}^M {M \choose \frac{NM + n}{N+1}} {L… Read More »Some Inner Product Calculations