Author Archives: pinkall

Consider the space $$C^0({\mathbb{Z}}^n)=\{f:{\mathbb{Z}}^n\to \mathbb{R}|f\text{ is bounded}\}.$$ Suppose we have a probability distribution $p$ on ${\mathbb{Z}}^n$ with mean zero: \begin{align*}p:\mathbb{Z}^n &\to \mathbb{R} \\ p(\mathbf{n})&\geq 0 \quad \text{for all}\quad \mathbf{n}\in \mathbb{Z}^n\\ \sum_{\mathbf{n}\in \mathbb{Z}^n} p(\mathbf{n})&=1 \\\sum_{\mathbf{n}\in \mathbb{Z}^n} … Continue reading →