  In this article, three models are considered, they are the
infinitely-many-neutral-alleles model \cite{MR615945}, infinite dimensional
diffusion associated with two-parameter Poisson-Dirichlet distribution
\cite{MR2596654} and the infinitely-many-alleles model with symmetric dominance
\cite{MR1626158}. The new representations of the transition transition
densities are obtained for the first two models. Lastly, the ergodic
inequalities of these three models are provided.
