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THE COMBINATORICS OF ALSALAMCHIHARA qLAGUERRE POLYNOMIALS
"... Abstract. We decribe various aspects of the AlSalamChihara qLaguerre polynomials. These include combinatorial descriptions of the polynomials, the moments, the orthogonality relation and a combinatorial interpretation of the linearization coefficients. Contents ..."
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Abstract. We decribe various aspects of the AlSalamChihara qLaguerre polynomials. These include combinatorial descriptions of the polynomials, the moments, the orthogonality relation and a combinatorial interpretation of the linearization coefficients. Contents
Conditional moments of qMeixner processes
, 2004
"... Abstract. We show that stochastic processes with linear conditional expectations and quadratic conditional variances are Markov, and their transition probabilities are related to a threeparameter family of orthogonal polynomials which generalize the Meixner polynomials. Special cases of these proce ..."
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Abstract. We show that stochastic processes with linear conditional expectations and quadratic conditional variances are Markov, and their transition probabilities are related to a threeparameter family of orthogonal polynomials which generalize the Meixner polynomials. Special cases of these processes are known to arise from the noncommutative generalizations of the Lévy processes. 1.
Moments, cumulants and diagram formulae for nonlinear functionals of random measures
, 2008
"... This survey provides a unified discussion of multiple integrals, moments, cumulants and diagram formulae associated with functionals of completely random measures. Our approach is combinatorial, as it is based on the algebraic formalism of partition lattices and Möbius functions. Gaussian and Poisso ..."
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Cited by 11 (7 self)
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This survey provides a unified discussion of multiple integrals, moments, cumulants and diagram formulae associated with functionals of completely random measures. Our approach is combinatorial, as it is based on the algebraic formalism of partition lattices and Möbius functions. Gaussian and Poisson measures are treated in great detail. We also present several combinatorial interpretations of some recent CLTs involving sequences of random variables belonging to a fixed Wiener chaos.
The Combinatorics of the AlSalamChihara qCharlier Polynomials
"... We describe various aspects of the AlSalamChihara qCharlier polynomials. These include combinatorial descriptions of the polynomials, the moments, the orthogonality relation and a combinatorial proof of Anshelevich’s recent result on the linearization coefficients. ..."
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Cited by 7 (3 self)
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We describe various aspects of the AlSalamChihara qCharlier polynomials. These include combinatorial descriptions of the polynomials, the moments, the orthogonality relation and a combinatorial proof of Anshelevich’s recent result on the linearization coefficients.
Séminaire Lotharingien de Combinatoire 69 (2013), Article B69b CYCLIC SIEVING PHENOMENA ON ANNULAR NONCROSSING PERMUTATIONS
"... Abstract. We showcyclicsievingphenomenaonannularnoncrossingpermutationswith given cycle types. We define annular qKreweras numbers, annular qNarayana numbers, and annular qCatalan numbers, and show that a sum of annular qKreweras numbers becomes an annular qNarayananumber and a sum of annular q ..."
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Abstract. We showcyclicsievingphenomenaonannularnoncrossingpermutationswith given cycle types. We define annular qKreweras numbers, annular qNarayana numbers, and annular qCatalan numbers, and show that a sum of annular qKreweras numbers becomes an annular qNarayananumber and a sum of annular qNarayananumbers becomes an annular qCatalan number. We also show that these polynomials are closely related to the cyclic sieving phenomena on annular noncrossing permutations. 1.
A PERMUTATION MODEL FOR FREE RANDOM VARIABLES AND ITS CLASSICAL ANALOGUE
"... Abstract. In this paper, we generalize a permutation model for free random variables which was first proposed by Biane in [B95b]. We also construct its classical probability analogue, by replacing the group of permutations with the group of subsets of a finite set endowed with the symmetric differen ..."
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Abstract. In this paper, we generalize a permutation model for free random variables which was first proposed by Biane in [B95b]. We also construct its classical probability analogue, by replacing the group of permutations with the group of subsets of a finite set endowed with the symmetric difference operation. These constructions provide new discrete approximations of the respective free and classical Wiener chaos. As a consequence, we obtain explicit examples of non random matrices which are asymptotically free or independent. The moments and the free (resp. classical) cumulants of the limiting distributions are expressed in terms of a special subset of (noncrossing) pairings. At the end of the paper we present some combinatorial applications of our results. hal00220460, version 3 11 Feb 2009