Remarks on global Monte Carlo algorithms

We calculate the acceptance probability of globally corrected Monte Carlo algorithms for the Gaussian model. For volume $N$ and step size $\delta$ we get for large $N$ the complementary error function of ${\delta }^3\sqrt{N}$. Although this result does not imply exponential suppression with ${\delta }^{6}N$ for all $\delta$, tuning prescriptions for the step size of the algorithm are not changed.