Greek letters in random staircase tableaux

TL;DR

This paper investigates staircase tableaux, a combinatorial object linked to probabilistic models and orthogonal polynomials, analyzing Greek letter appearances and their limiting distributions.

Contribution

It introduces a probabilistic framework to analyze parameters of staircase tableaux, revealing limiting distributions for Greek letter occurrence statistics.

Findings

Derived limiting distributions for Greek letter appearances

Developed a probabilistic analysis method for staircase tableaux

Connected staircase tableaux with Askey-Wilson polynomials

Abstract

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.