In Wikipedia's description of the Metropolis algorithm, I see the phrase:
The probability of rejection increases exponentially as a function of the number of dimensions.
This obviously can't mean $\Pr[\text{rejection}] \propto c^d$ where $d$ is the number of dimensions and $c > 0$ is a constant, so what does the phrase mean here?
Does it mean $\Pr[\text{acceptance}] \propto c^{-d}$ for some $c > 0$, or does it mean something else...?
And if it had said "decrease exponentially" then what would that have meant?