相关论文: Martingales and character ratios

The combination of the group ring setting with the methods of character theory allows an elegant and powerful analysis of various combinatorial structures, via their character sums. These combinatorial structures include difference sets,…

In this investigation of character tables of finite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy classes. For the symmetric groups we find unexpected properties of characters on…

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…

We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration…

We consider asymptotics of ratios of random characteristic polynomials associated with orthogonal polynomial ensembles. Under some natural conditions on the measure in the definition of the orthogonal polynomial ensemble we establish a…

We compute correlation functions of inverse powers and ratios of characteristic polynomials for random matrix models with complex eigenvalues. Compact expressions are given in terms of orthogonal polynomials in the complex plane as well as…

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…

We established the rate of convergence in the central limit theorem for stopped sums of a class of martingale difference sequences.

On a compact group the Haar probability measure plays the role of uniform distribution. The entropy and rate distortion theory for this uniform distribution is studied. New results and simplified proofs on convergence of convolutions on…

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…

The main result of the article reads: the distribution of a continuous starting from zero local martingale whose quadratic characteristic is almost surely absolutely continuous with respect to some non-random increasing continuous function…

We study connections between the topology of generic character varieties of fundamental groups of punctured Riemann surfaces, Macdonald polynomials, quiver representations, Hilbert schemes on surfaces, modular forms and multiplicities in…

Stanley introduces polynomials which help evaluate symmetric group characters and conjectures that the coefficients of the polynomials are positive. Stanley later gives a conjectured combinatorial interpretation for the coefficients of the…

In this paper, we first show that the irreducible characters of a quotient table algebra modulo a normal closed subset can be viewed as the irreducible characters of the table algebra itself. Furthermore, we define the character products…

In this article we prove martingale type pointwise convergence theorems pertaining to tensor product splines defined on $d$-dimensional Euclidean space ($d$ is a positive integer), where conditional expectations are replaced by their…

We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the martingale, we prove that normalized moments of…

We compute averages of products and ratios of characteristic polynomials associated with Orthogonal, Unitary, and Symplectic Ensembles of Random Matrix Theory. The pfaffian/determinantal formulas for these averages are obtained, and the…

Invariance properties of semimartingales on Lie groups under a family of random transformations are defined and investigated, generalizing the random rotations of the Brownian motion. A necessary and sufficient explicit condition…

For orthogonal polynomials defined by compact Jacobi matrix with exponential decay of the coefficients, precise properties of orthogonality measure is determined. This allows showing uniform boundedness of partial sums of orthogonal…

We review the theory of martingales as applied to stochastic thermodynamics and stochastic processes in physics more generally.