  We describe ergodic properties of some Metropolis-Hastings (MH) algorithms
for heavy-tailed target distributions. The analysis usually falls into
sub-geometric ergodicity framework but we prove that the mixed preconditioned
Crank-Nicolson (MpCN) algorithm has geometric ergodicity even for heavy-tailed
target distributions. This useful property comes from the fact that the MpCN
algorithm becomes a random-walk Metropolis algorithm under suitable
transformation.
