  We consider Robinson-Schensted-Knuth algorithm applied to a random input and
study the growth of the bottom rows of the corresponding Young diagrams. We
prove multidimensional Poisson limit theorem for the resulting Plancherel
growth process. In this way we extend the result of Aldous and Diaconis to more
than just one row. This result can be interpreted as convergence of the
multi-line Hammersley process to its stationary distribution which is given by
a collection of independent Poisson point processes.
