Paper Info
Title
The asymptotic distribution of symbols on diagonals of random weighted staircase tableaux.
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 kth diagonal where k is fixed. In particular, we prove that the distribution of the number of alpha's (beta's) on the kth diagonal, k > 1, is asymptotically Poisson with parameter 1/2. In addition, we prove that symbols on the kth diagonal are asymptotically independent and thus, collectively follow the Poisson distribution with parameter 1. (C) 2016 Wiley Periodicals, Inc.
Year
DOI
Venue
2016
10.1002/rsa.20665
RANDOM STRUCTURES & ALGORITHMS
Keywords
Field
DocType
staircase tableaux,asymmetric simple exclusion process,Poisson distribution
Diagonal,Discrete mathematics,Combinatorics,Asymmetric simple exclusion process,Polynomial,Poisson distribution,Conjecture,Mathematics,Asymptotic distribution
Journal
Volume
Issue
ISSN
49.0
SP4.0
1042-9832
Citations 
PageRank 
References 
0
0.34
1
Authors
1
Name
Order
Citations
PageRank
amanda lohss100.68