Cumulants, lattice paths, and orthogonal polynomials

被引：13

作者：

Lehner, F ^{[1
]}

机构：

[1] Graz Univ Technol, Inst Math C, A-8010 Graz, Austria

来源：

DISCRETE MATHEMATICS | 2003年 / 270卷 / 1-3期

关键词：

cumulants; lattice path combinatorics; Motzkin paths; Lukasiewicz paths; continued fractions; Hankel determinants; orthogonal polynomials;

D O I：

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

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A formula expressing free cumulants in terms of Jacobi parameters of the corresponding orthogonal polynomials is derived. It combines Flajolet's theory of continued fractions and the Lagrange inversion formula. For the converse we discuss Gessel-Viennot theory to express Hankel determinants in terms of various cumulants. (C) 2003 Elsevier B.V. All rights reserved.

引用

页码：177 / 191

页数：15

共 29 条

[1] Interacting Fock spaces and Gaussianization of probability measures [J].