  The choice of the increment distribution is crucial for the random-walk
Metropolis-Hastings (RWM) algorithm. In this paper we study the optimal choice
in high-dimension setting among all possible increment distributions. The
conclusion is rather counter intuitive, but the optimal rate of convergence is
attained by the usual choice, the normal distribution as the increment
distribution. In particular, no heavy-tailed increment distribution can improve
the rate.
