Cumulants, lattice paths, and orthogonal polynomials

Details Cumulants, lattice paths, and orthogonal polynomials Cumulants, lattice paths, and orthogonal polynomials

2001-10-02

arxiv.org/abs/math/0110031v2

Discrete Math. 270 (2003), no. 1-3, 177--191

Mathematics

Combinatorics

11 pages, AMS LaTeX, uses pstricks; revised according to referee's suggestions, in particular cut down last section and correc

Scientific paper

10.1016/S0012-365X(02)00834-8

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.

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