相关论文: Composite parameterization and Haar measure for al…
A generalized Hubbard-Stratonovitch transformation relating an integral over random unitary N times N matrices to an integral over Efetov's unitary sigma model manifold, is introduced. This transformation adapts the supersymmetry method to…
According to the classification scheme of the generalized random matrix ensembles, we present various kinds of concrete examples of the generalized ensemble, and derive their joint density functions in an unified way by one simple formula…
We study the combinatorics of the contributions to the form factor of the group U(N) in the large $N$ limit. This relates to questions about semiclassical contributions to the form factor of quantum systems described by the unitary…
The purpose of this paper is to give explicit constructions of unitary $t$-designs in the unitary group $U(d)$ for all $t$ and $d$. It seems that the explicit constructions were so far known only for very special cases. Here explicit…
We consider a unitary representation of the Dihedral group $D_{2n}% =\mathbb{Z}_{n}\rtimes\mathbb{Z}_{2}$ obtained by inducing the trivial character from the co-normal subgroup $\left\{0\right\}\rtimes\mathbb{Z}_{2}.$ This representation is…
I adapt a recently introduced method for integrating over the unitary group (S. Aubert and C.S. Lam, J.Math.Phys. 44, 6112-6131 (2003)) to the orthogonal group. I derive explicit formulas for a number of one, two and three-vector integrals,…
Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…
It is known that a unitary matrix can be decomposed into a product of reflections, one for each dimension, and the Haar measure on the unitary group pushes forward to independent uniform measures on the reflections. We consider the sequence…
We apply methods from strict quantization of solvable symmetric spaces to obtain universal deformation formulae for actions of a class of solvable Lie groups. We also study compatible co-products by generalizing the notion of smash product…
This paper collects miscellaneous results about the group SU(1,1) that are helpful in applications in quantum optics. Moreover, we derive two new results, the first is about the approximability of SU(1,1) elements by a finite set of…
We introduce generalised orbit algebras. The purpose here is to measure how some combinatorial properties can characterize the action of a group of permutations on the subsets. The similarity with orbit algebras is such that it took the…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
In this paper, we provide a complete regularity analysis for an abstract system of coupled hyperbolic and parabolic equations in a complex Hilbert space. We are able to decompose the unit square of the parameters into three parts where the…
This paper is concerned with complex eigenvalues of truncated unitary quaternion matrices equipped with the Haar measure. The joint eigenvalue probability density function is obtained for truncations of any size. We also obtain the spectral…
Uniform measures are the functionals on the space of bounded uniformly continuous functions that are continuous on every bounded uniformly equicontinuous set. This paper describes the role of uniform measures in the study of convolution on…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
Feynman's diagrammatic series is a common language for a formally exact theoretical description of systems of infinitely-many interacting quantum particles, as well as a foundation for precision computational techniques. Here we introduce a…
By using the notion of a Haar ambivalent set introduced by Balka, Buczolich and Elekes (2012), essentially new classes of statistical structures having objective and strong objective estimates of unknown parameters are introduced in a…
In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…
This survey note describes a brief systemic view to approaches for evaluation of hierarchical composite (modular) systems. The list of considered issues involves the following: (i) basic assessment scales (quantitative scale, ordinal scale,…