2014/04/14 by Paweł Hitczenko, Pawel Hitczenko, Hitczenko, Pawel +2 · 1 citation
Mathematics · #05A16 #05B30 #60F05 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.CO #math.PR #msc:05A16 #msc:05B30 #msc:60F05
paper · pdf · doi:10.48550/arxiv.1404.3446
arxiv created 2014/04/14 · openalex publication_date 2014/04/14 · arxiv updated 2014/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study staircase tableaux, a combinatorial object introduced due to its connections with the asymmetric exclusion process (ASEP) and Askey-Wilson polynomials. Due to their interesting connections, staircase tableaux have been the object of study in many recent papers. More specific to this paper, the distribution of various parameters in random staircase tableaux has been studied. There have been interesting results on parameters along the main diagonal, however, no such results have appeared for other diagonals. It was conjectured that the distribution of the number of symbols along the kth diagonal is asymptotically Poisson as k and the size of the tableau tend to infinity. We partially prove this conjecture; more specifically we prove it for the second main diagonal.