I want to know whether or not such high dimensional distribution $P$ exists?
Given a distribution $P$ in $\mathbb{R}^d$, we sample $n$ vectors $z_1, z_2, ..., z_n$ from it, and we have $n << d$.
For each pair of $z_i$ and $z_j$, we have $\cos(z_i, z_j) \approx \alpha$, where $\alpha$ is a positive scalar.
I know when $\alpha = 0$ or $\alpha=1$ such distribution is easy to find. But is there a way to construct such distribution when $\alpha=0.3$ or $\alpha=0.5$?