  We consider the simplest split-merge Markov operator $T$ on the
infinite-dimensional simplex $\Sigma_1$ of monotone non-negative sequences with
unit sum. For a sequence $x\in\Sigma_1$, it picks a size-biased sample (with
replacement) of two elements of $x$; if these elements are distinct, it merges
them and reorders the sequence, and if the same element is picked twice, it
splits this element uniformly into two parts and reorders the sequence. We
prove that the means along the $T$-trajectory of the $\de$-measure at the
vector $(1,0,0,{...})$ converge to the Poisson--Dirichlet distribution PD(1).
