相关论文: A Generalization of Random Matrix Ensemble I: Gene…
This is an introductory note concerning the distribution vectors in a unitary representation of a Lie group. We discuss the definition of matrix coefficients associated with a pair of distributions and how one can compute them. Most of the…
We investigate density of various subalgebras of regular generalized functions in the special Colombeau algebra of generalized functions.
We present an overview of the Density Matrix Renormalization Group and its connections to Quantum Groups, Matrix Products and Conformal Field Theory. We emphasize some common formal structures in all these theories. We also propose…
Explicit expressions for multimatrix models with complex and unitary matrices allows to couple these models with well-known unitary, orthogonsl and sympletic ensembles. We consider examples of such mixed ensembles which are solvable in the…
Correlation functions for matrix ensembles with orthogonal and unitarysymplectic rotation symmetry are more complicated to calculate than in the unitary case. The supersymmetry method and the orthogonal polynomials are two techniques to…
For many applications, an ensemble of base classifiers is an effective solution. The tuning of its parameters(number of classes, amount of data on which each classifier is to be trained on, etc.) requires G, the generalization error of a…
General regression and classification models are constructed as linear combinations of simple rules derived from the data. Each rule consists of a conjunction of a small number of simple statements concerning the values of individual input…
A random matrix ensemble incorporating both GUE and Poisson level statistics while respecting $U(N)$ invariance is proposed and shown to be equivalent to a system of noninteracting, confined, one dimensional fermions at finite temperature.
We consider random stochastic matrices $M$ with elements given by $M_{ij}=|U_{ij}|^2$, with $U$ being uniformly distributed on one of the classical compact Lie groups or associated symmetric spaces. We observe numerically that, for large…
Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.
A statistical description of part of a many body system often requires a non-Hermitian random matrix ensemble with nature and strength of randomness sensitive to underlying system conditions. For the ensemble to be a good description of the…
In these lectures we discuss some elementary concepts in connection with the theory of symmetric spaces applied to ensembles of random matrices. We review how the relationship between random matrix theory and symmetric spaces can be used in…
Generic computability has been studied in group theory and we now study it in the context of classical computability theory. A set A of natural numbers is generically computable if there is a partial computable function f whose domain has…
We exhibit an explicit formula for the spectral density of a (large) random matrix which is a diagonal matrix whose spectral density converges, perturbated by the addition of a symmetric matrix with Gaussian entries and a given (small)…
We present a common ground for infinite sums, unordered sums, Riemann/Lebesgue integrals, arc length and some generalized means. It is based on extending functions on finite sets using Hausdorff metric in a natural way.
This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…
A generally intelligent learner should generalize to more complex tasks than it has previously encountered, but the two common paradigms in machine learning -- either training a separate learner per task or training a single learner for all…
We consider random non-hermitean matrices in the large $N$ limit. The power of analytic function theory cannot be brought to bear directly to analyze non-hermitean random matrices, in contrast to hermitean random matrices. To overcome this…
We compute the spectral density for ensembles of of sparse symmetric random matrices using replica, managing to circumvent difficulties that have been encountered in earlier approaches along the lines first suggested in a seminal paper by…
Conventional approximations to Bayesian inference rely on either approximations by statistics such as mean and covariance or by point particles. Recent advances such as the ensemble Gaussian mixture filter have generalized these notions to…