Weighted random staircase tableaux
Pawel Hitczenko, Svante Janson

TL;DR
This paper explores the combinatorial properties of weighted staircase tableaux, generalizing previous results, analyzing their structure, and connecting them to models like the asymmetric exclusion process and Eulerian polynomials.
Contribution
It introduces a general weighted model for staircase tableaux, derives limiting laws, and studies the associated polynomial families, extending prior specific case analyses.
Findings
Derived limiting distributions for symbol counts in random tableaux.
Established connections between weighted tableaux and Eulerian polynomial generalizations.
Analyzed structural properties of random staircase tableaux under various weight regimes.
Abstract
This paper concerns a relatively new combinatorial structure called staircase tableaux. They were introduced in the context of the asymmetric exclusion process and Askey--Wilson polynomials, however, their purely combinatorial properties have gained considerable interest in the past few years. In this paper we further study combinatorial properties of staircase tableaux. We consider a general model of staircase tableaux in which symbols that appear in staircase tableaux may have arbitrary positive weights. Under this general model we derive a number of results. Some of our results concern the limiting laws for the number of appearances of symbols in a random staircase tableaux. They generalize and subsume earlier results that were obtained for specific values of the weights. One advantage of our generality is that we may let the weights approach extreme values of zero or infinity…
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