AbstractA 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
AbstractFor a fixed positive integer ℓ, let f(n,ℓ) denote the number of lattice paths that use the s...
We provide a unifying polynomial expression giving moments in terms of cumulants, and vice versa, ho...
International audienceFree cumulants were introduced by Speicher as a proper analog of classical cum...
AbstractA formula expressing free cumulants in terms of Jacobi parameters of the corresponding ortho...
AbstractWe show that the universal continued fraction of the Stieltjes-Jacobi type is equivalent to ...
We define an infinite sequence of generalizations, parametrized by an integer m ≥ 1, of the Stieltj...
AbstractThis paper extends Flajolet's (Discrete Math. 32 (1980), 125–161) combinatorial theory of co...
AbstractWe provide a unifying polynomial expression giving moments in terms of cumulants, and vice v...
AbstractWe study cumulants by Umbral Calculus. Various formulae expressing cumulants by umbral funct...
We prove a constant term theorem which is useful for finding weight polynomials for Ballot/Motzkin p...
We establish the functional relations between generating series of higher order free cumulants and m...
AbstractWe derive a formula for expressing free cumulants whose entries are products of random varia...
We consider the Motzkin paths which are simple combinatorial objects appearing in many contexts. The...
In this article, we revisit and extend a list of formulas based on lattice path surgery: cut-and-pas...
AbstractWe develop a general context for the computation of the determinant of a Hankel matrix Hn = ...
AbstractFor a fixed positive integer ℓ, let f(n,ℓ) denote the number of lattice paths that use the s...
We provide a unifying polynomial expression giving moments in terms of cumulants, and vice versa, ho...
International audienceFree cumulants were introduced by Speicher as a proper analog of classical cum...
AbstractA formula expressing free cumulants in terms of Jacobi parameters of the corresponding ortho...
AbstractWe show that the universal continued fraction of the Stieltjes-Jacobi type is equivalent to ...
We define an infinite sequence of generalizations, parametrized by an integer m ≥ 1, of the Stieltj...
AbstractThis paper extends Flajolet's (Discrete Math. 32 (1980), 125–161) combinatorial theory of co...
AbstractWe provide a unifying polynomial expression giving moments in terms of cumulants, and vice v...
AbstractWe study cumulants by Umbral Calculus. Various formulae expressing cumulants by umbral funct...
We prove a constant term theorem which is useful for finding weight polynomials for Ballot/Motzkin p...
We establish the functional relations between generating series of higher order free cumulants and m...
AbstractWe derive a formula for expressing free cumulants whose entries are products of random varia...
We consider the Motzkin paths which are simple combinatorial objects appearing in many contexts. The...
In this article, we revisit and extend a list of formulas based on lattice path surgery: cut-and-pas...
AbstractWe develop a general context for the computation of the determinant of a Hankel matrix Hn = ...
AbstractFor a fixed positive integer ℓ, let f(n,ℓ) denote the number of lattice paths that use the s...
We provide a unifying polynomial expression giving moments in terms of cumulants, and vice versa, ho...
International audienceFree cumulants were introduced by Speicher as a proper analog of classical cum...
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