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Rephrasing expansion (slightly). Consider the following slightly tweaked version of the usual definition of a (spectral) expander graph. (We write a weighted graph as $(V,\beta)$, where the weight $\...

Let $\Gamma=(V,E)$ be an undirected graph of degree $d$. (Say $d$ is a large constant and the number of vertices $n=|V|$ is much larger.) Let $W_0$ be the space of functions $f:V\to \mathbb{C}$ with ...