相关论文: Sum rules for characters from character-preservati…

We obtain transformation formulas for quadratic character sums with quartic and cubic polynomial arguments.

We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with Hermitian matrices whose elements perform a random walk in the space of complex numbers, satisfy certain partial…

We study additive double character sums over two subsets of a finite field. We show that if there is a suitable rational self-map of small degree of a set $D$, then this set contains a large subset $U$ for which the standard bound on the…

We show that various identities from [1] and [3] involving Gould-Hopper polynomials can be deduced from the real but also complex orthogonal invariance of multivariate Gaussian distributions. We also deduce from this principle a useful…

We study the representation theory of a certain finite group for which Kloosterman sums appear as character values. This leads us to consider a concrete family of commuting hermitian matrices which have Kloosterman sums as eigenvalues.…

Character polynomials are used to study the restriction of a polynomial representation of a general linear group to its subgroup of permutation matrices. A simple formula is obtained for computing inner products of class functions given by…

In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…

We derive exact analytic expressions for the distributions of eigenvalues and singular values for the product of an arbitrary number of independent rectangular Gaussian random matrices in the limit of large matrix dimensions. We show that…

A few elementary estimates of a basic character sum over the prime numbers are derived here. These estimates are nontrivial for character sums modulo large q. In addition, an omega result for character sums over the primes is also included.

We present fermionic sum representation for the general Virasoro character of the unitary minimal superconformal series ($N=1$). Example of the corresponding ``finitizated" identities relating corner transfer matrix polynomials with…

We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…

Character expansions are among the most important approaches to modern quantum field theory, which substitute integrals by combinations of peculiar special functions from the Schur-Macdonald family. These formulas allow various…

We extend the close interplay between continued fractions, orthogonal polynomials, and Gaussian quadrature rules to several variables in a special but natural setting which we characterize in terms of moment sequences. The crucial condition…

We obtain explicit bounds on the moments of character sums, refining estimates of Montgomery and Vaughan. As an application we obtain results on the distribution of the maximal magnitude of character sums normalized by the square root of…

In classical random matrix theory the Gaussian and chiral Gaussian random matrix models with a source are realized as shifted mean Gaussian, and chiral Gaussian, random matrices with real $(\beta = 1)$, complex ($\beta = 2)$ and real…

In this paper, we obtain formulas for the number of representations of positive integers as sums of arbitrarily many squares (and other polygonal numbers) with a certain natural weighting. The resulting weighted sums give Fourier…

We develop methods for systematic construction of superintegrable polynomials in matrix/eigenvalue models. Our consideration is based on a tight connection of superintegrable property of Gaussian Hermitian model and $W_{1 + \infty}$ algebra…

We summarize the recent results about complete solvability of Hermitian and rectangular complex matrix models. Partition functions have very simple character expansions with coefficients made from dimensions of representation of the linear…

We derive a common mathematical formulation for the eigenfunction statistics of Hermitian operators, represented by a multi-parametric probability density. The system-information in the formulation enters through two parameters only,…

Many aspects of the asymptotics of Plancherel distributed partitions have been studied in the past fifty years, in particular the limit shape, the distribution of the longest rows, connections with random matrix theory and characters of the…