  In this paper we study a relatively new combinatorial object called staircase
tableaux. Staircase tableaux were introduced by Corteel and Williams in the
connection with Asymmetric Exclusion Process and has since found interesting
connections with Askey - Wilson polynomials. We develop a probabilistic
approach that allows us to analyze several parameters of a randomly chosen
staircase tableaux of a given size. In particular, we obtain limiting
distributions for statistics associated with appearances of Greek letters in
staircase. tableaux.
