[math] \newcommand{\mathds}{\mathbb}[/math]

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Prove that, if [math]g_{ij}[/math] are the standard coordinates of [math]S_N\subset O_N[/math],

[[math]] {\rm law}(g_{11}+\ldots +g_{ss})=\frac{s!}{N!}\sum_{p=0}^s\frac{(N-p)!}{(s-p)!} \cdot\frac{\left(\delta_1-\delta_0\right)^{*p}}{p!} [[/math]]

and deduce from this that such variables become Poisson, with [math]N\to\infty[/math].