Probabilistic consequences of some polynomial recurrences. Issue 4 (21st October 2018)

• Record Type: Journal Article
• Authors: Hitczenko, Paweł; Lohss, Amanda
• Is Part Of: Random structures & algorithms. Volume 53:Issue 4(2018)
• Page Start: 652
• Page End: 666
• Publication Date: 2018-10-21
• Subjects: generating polynomial -- recurrence -- tree‐like tableaux; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20820
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract : In this paper, we consider sequences of polynomials that satisfy certain recurrences. Our interest is motivated by the fact that polynomials satisfying such recurrences frequently appear as generating polynomials of integer valued random variables that are of interest in discrete mathematics. In particular, we will use our approach to show that the number of diagonal boxes in symmetric tree‐like tableaux is asymptotically normal. This extends earlier results of Aval, Boussicault and Nadeau, who found the asymptotics of the expected number of diagonal boxes. Through our discussion, we establish a general framework to approach such recurrences and prompt a generalization of the probabilistic consequences of them.