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Jucys-Murphy elements, orthogonal matrix integrals, and Jack measures, ArXiv 1001.2345
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Jack polynomials and free cumulants
, 802
"... We study the coefficients in the expansion of Jack polynomials in terms of power sums. We express them as polynomials in the free cumulants of the transition measure of an anisotropic Young diagram. We conjecture that such polynomials have nonnegative integer coefficients. This extends recent result ..."
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We study the coefficients in the expansion of Jack polynomials in terms of power sums. We express them as polynomials in the free cumulants of the transition measure of an anisotropic Young diagram. We conjecture that such polynomials have nonnegative integer coefficients. This extends recent results about normalized characters of the symmetric group.
Class expansion of some symmetric functions
- in Jucys-Murphy elements, Arxiv preprint arXiv:1005.2346 (2010), URL http://arxiv.org/abs
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An Inductive Proof of the Berry-Esseen Theorem for Character Ratios
, 2005
"... Abstract: Bolthausen used a variation of Stein’s method to give an inductive proof of the Berry-Esseen theorem for sums of independent, identically distributed random variables. We modify this technique to prove a Berry-Esseen theorem for character ratios of a random representation of the symmetric ..."
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Abstract: Bolthausen used a variation of Stein’s method to give an inductive proof of the Berry-Esseen theorem for sums of independent, identically distributed random variables. We modify this technique to prove a Berry-Esseen theorem for character ratios of a random representation of the symmetric group on transpositions. An analogous result is proved for Jack measure on partitions.
Two new families of q-positive integers
, 2004
"... Abstract. Let n, p, k be three positive integers. We prove that the rational fractions of q: 1−k −p p−n q, q, q q, q1−n] q; qk+1 and q ∣ (n−p)p 1−k −p p−n n q, q, q 3φ2 k q, q1−n] q; q ..."
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Abstract. Let n, p, k be three positive integers. We prove that the rational fractions of q: 1−k −p p−n q, q, q q, q1−n] q; qk+1 and q ∣ (n−p)p 1−k −p p−n n q, q, q 3φ2 k q, q1−n] q; q
