I read that rejection sampling might fail in high dimensional settings, as the rejection rate becomes too low. Intuitively - i can understand this - but i would like to understand the formal proof as well. From the excellent answer on How does the proof of Rejection Sampling make sense? I understand that the rejection rate is $1/M$. I understand as well that it is required that $\sigma_q > \sigma_p$ and that in D dimensions hence M should be $(\sigma_p/\sigma_q)^D$, but i am struggling to combines these facts to e.g. proof the example. Any tips welcome!