Rate optimality of Random walk Metropolis algorithm in high-dimension   with heavy-tailed target distribution
  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. 
Kengo Kamatani
stat.ME math.PR