The asymptotic distribution of symbols on diagonals of random weighted staircase tableaux. Issue 4 (2nd August 2016)

• Record Type: Journal Article
• Authors: Lohss, Amanda
• Is Part Of: Random structures & algorithms. Volume 49:Issue 4(2016)
• Page Start: 795
• Page End: 818
• Publication Date: 2016-08-02
• Subjects: staircase tableaux -- asymmetric simple exclusion process -- Poisson distribution; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20665
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract: Staircase tableaux are combinatorial objects that were first introduced due to a connection with the asymmetric simple exclusion process (ASEP) and Askey‐Wilson polynomials. Since their introduction, staircase tableaux have been the object of study in many recent papers. Relevant to this paper, Hitczenko and Janson proved that distribution of parameters on the first diagonal is asymptotically normal. In addition, they conjectured that other diagonals would be asymptotically Poisson. Since then, only the second and the third diagonal were proven to follow the conjecture. This paper builds upon those results to prove the conjecture for the k th diagonal where k is fixed. In particular, we prove that the distribution of the number of α 's ( β 's) on the k th diagonal, k > 1, is asymptotically Poisson with parameter 1/2. In addition, we prove that symbols on the k th diagonal are asymptotically independent and thus, collectively follow the Poisson distribution with parameter 1. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 795–818, 2016