相关论文: A Generalization of Random Matrix Ensemble I: Gene…

Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the {\it possibility of approximation}. Is the given…

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…

The distribution of the sum of r-th power of standard normal random variables is a generalization of the chi-squared distribution. In this paper, we represent the probability density function of the random variable by an one-dimensional…

A class of spherical functions is studied which can be viewed as the matrix generalization of Bessel functions. We derive a recursive structure for these functions. We show that they are only special cases of more general radial functions…

The most efficient weights for Markov chain Monte Carlo calculations of physical observables are not necessarily those of the canonical ensemble. Generalized ensembles, which do not exist in nature but can be simulated on computers, lead…

We propose new classes of random matrix ensembles whose statistical properties are intermediate between statistics of Wigner-Dyson random matrices and Poisson statistics. The construction is based on integrable N-body classical systems with…

In the paper, the authors introduce a matrix-parametrized generalization of the multinomial probability mass function that involves a ratio of several multivariate gamma functions. They show the logarithmic complete monotonicity of this…

Assuming a view of the Random Forest as a special case of a nested ensemble of interchangeable modules, we construct a generalisation space allowing one to easily develop novel methods based on this algorithm. We discuss the role and…

A given density matrix may be represented in many ways as a mixture of pure states. We show how any density matrix may be realized as a uniform ensemble. It has been conjectured that one may realize all probability distributions that are…

Machine Reading Comprehension (MRC) is an active field in natural language processing with many successful developed models in recent years. Despite their high in-distribution accuracy, these models suffer from two issues: high training…

This paper examines the classical matching distribution arising in the "problem of coincidences". We generalise the classical matching distribution with a preliminary round of allocation where items are correctly matched with some fixed…

We introduce a class of association schemes that generalizes the Hamming scheme. We derive generating functions for their eigenvalues, and use these to obtain a version of MacWilliams theorem.

The density of state for a complex $N\times N$ random matrix coupled to an external deterministic source is considered for a finite N, and a compact expression in an integral representation is obtained.

This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution…

We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…

Combining the derivative operator with a binomial sum from the telescoping method, we establish a family of summation formulas involving generalized harmonic numbers.

A new method involving particle diagrams is introduced and developed into a rigorous framework for carrying out embedded random matrix calculations. Using particle diagrams and the attendant methodology including loop counting it becomes…

We will generalize the concept of aggregation function for mathematical structures as a certain function between quantales. In fact, these functions turn to be exactly the lax morphism of quantales. This provides a global framework for the…

An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…

Ensembles of neural networks have been shown to give better performance than single networks, both in terms of predictions and uncertainty estimation. Additionally, ensembles allow the uncertainty to be decomposed into aleatoric (data) and…