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For high enough dimension $n$, the base cell of the Voronoi partition of a lattice $L_n$ in $\mathbb{R}^n$ picked randomly from the Siegel ensemble typically has some unit-ball-like properties: it ...

Suppose $\mathcal{F}=\left\{f\in L^2([a,b]): 0<\underline{c}\leq f\leq\overline{c} \right\}$. Consider the following transformation $$\tilde{\mathcal{F}} := \left\{\frac{f}{\int f d\mu}: f\in \...