相关论文: Asymptotics of Jack polynomials as the number of v…

We describe the asymptotic behavior of the multivariate BC-type Jacobi polynomials as the number of variables and the Young diagram indexing the polynomial go to infinity. In particular, our results describe the approximation of the…

In this paper we study the asymptotic behavior of the (skew) Macdonald and Jack symmetric polynomials as the number of variables grows to infinity. We characterize their limits in terms of certain variational problems. As an intermediate…

In this note, we study the asymptotic of spherical integrals, which are analytical extension in index of the normalized Schur polynomials for $\beta =2$ , and of Jack symmetric polynomials otherwise. Such integrals are the multiplicative…

We introduce Jack (unitary) characters and prove two kinds of formulas that are suitable for their asymptotics, as the lengths of the signatures that parametrize them go to infinity. The first kind includes several integral representations…

We prove several asymptotic results for partial and false theta functions arising from Jacobi forms, as the modular variable $\tau$ tends to $0$ along the imaginary axis, and the elliptic variable $z$ is unrestricted in the complex plane.…

Jack characters are a one-parameter deformation of the characters of the symmetric groups; a deformation given by the coefficients in the expansion of Jack symmetric functions in the basis of power-sum symmetric functions. We study Jack…

We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found in these bases, including Eulerian…

We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found in these bases, including Eulerian…

We study the asymptotic behavior of two statistics defined on the symmetric group S_n when n tends to infinity: the number of elements of S_n having k records, and the number of elements of S_n for which the sum of the positions of their…

We develop a new method for studying the asymptotics of symmetric polynomials of representation-theoretic origin as the number of variables tends to infinity. Several applications of our method are presented: We prove a number of theorems…

Motivated by Stanley's conjecture on the multiplication of Jack symmetric functions, we prove a couple of identities showing that skew Jack symmetric functions are semi-invariant up to translation and rotation of a $\pi$ angle of the skew…

We construct a generalization of the theory of symmetric functions involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under the diagonal…

We prove two theorems. Theorem 1 gives the meromorphic continuation of the multiple zeta function to the whole space. In Theorem 2, we prove asymptotic behavior near the non-positive integers.

Spectral properties of Jacobi operators $J$ are intimately related to an asymptotic behavior of the corresponding orthogonal polynomials $P_{n}(z)$ as $n\to\infty$. We study the case where the off-diagonal coefficients $a_{n}$ and,…

We provide an asymptotic expansion for $\sum_{k=1}^n \left\{\sqrt{k}\right\}$. In the same spirit, we discuss the case of n-th root and it relation to special values of Riemman's zeta function.

We obtain the asymptotic expansion of the Voigt functions $K(x,y)$ and $L(x,y)$ for large (real) values of the variables $x$ and $y$, paying particular attention to the exponentially small contributions. A Stokes phenomenon is encountered…

We consider a deformation of Kerov character polynomials, linked to Jack symmetric functions. It has been introduced recently by M. Lassalle, who formulated several conjectures on these objects, suggesting some underlying combinatorics. We…

Here we examine the number of ways to partition an integer $n$ into $k$th powers when $n$ is large. Simplified proofs of some asymptotic results of Wright are given using the saddle-point method, including exact formulas for the expansion…

We compute the Harish-Chandra $c$-function for a generic class of rank-one purely non-compact Riemannian symmetric superspaces $X=G/K$ in terms of Euler $\Gamma$ functions, proving that it is meromorphic. Compared to the even case, the…

Jack polynomials in superspace, orthogonal with respect to a ``combinatorial'' scalar product, are constructed. They are shown to coincide with the Jack polynomials in superspace, orthogonal with respect to an ``analytical'' scalar product,…