English

Doron Gepner's Statistics on Words in {1,2,3} is (most probably) Asymptotically Logistic

Combinatorics 2016-04-05 v1

Abstract

Doron Gepner's word statistics, that came up in his research in conformal field theory, is studied and it is conjectured that its scaled limiting distribution is the Logistic distribution. We support this by proving rigorously that the scaled limits of the first twelve moments do indeed converge to those of the Logistic distribution. This is surprising, since Gepner's statistics is a natural analog of the classical statistics called the number of inversion, that is known to be asymptotically normal.

Keywords

Cite

@article{arxiv.1604.00663,
  title  = {Doron Gepner's Statistics on Words in {1,2,3} is (most probably) Asymptotically Logistic},
  author = {Doron Zeilberger},
  journal= {arXiv preprint arXiv:1604.00663},
  year   = {2016}
}

Comments

11 pages. Accompanied by a Maple package, GEPNER.txt, and sample input and output files available from http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/gepner.html