Cumulants, lattice paths, and orthogonal polynomials
Combinatorics
2007-05-23 v2
Abstract
A formula expressing free cumulants in terms of the Jacobi parameters of the corresponding orthogonal polynomials is derived. It combines Flajolet's theory of continued fractions and Lagrange inversion. For the converse we discuss Gessel-Viennot theory to express Hankel determinants in terms of various cumulants.
Cite
@article{arxiv.math/0110031,
title = {Cumulants, lattice paths, and orthogonal polynomials},
author = {Franz Lehner},
journal= {arXiv preprint arXiv:math/0110031},
year = {2007}
}
Comments
11 pages, AMS LaTeX, uses pstricks; revised according to referee's suggestions, in particular cut down last section and corrected some wrong attributions