The asymptotic distribution of symbols on diagonals of random weighted staircase tableaux

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 α's (β'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. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 795–818, 2016

• Publication year

  2015

• Venue

  Random Struct. Algorithms

• Publication date

  2015-12-01

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1002/rsa.20665arXiv 1512.00329
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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