Related papers: On the Unification of Random Matrix Theories
Around 1950, Wigner introduced the idea of modelling physical reality with an ensemble of random matrices while studying the energy levels of heavy atomic nuclei. Since then, the field of random-matrix theory has grown tremendously, with…
Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify…
Estimating quantum amplitude, or the overlap between two quantum states, is a fundamental task in quantum computing and underpins numerous quantum algorithms. In this work, we introduce a novel algorithmic framework for quantum amplitude…
In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of…
New insight into the correspondence between Quantum Chaos and Random Matrix Theory is gained by developing a semiclassical theory for the autocorrelation function of spectral determinants. We study in particular the unitary operators which…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
In this article, we present a novel approach to investigating entanglement in the context of quantum computing. Our methodology involves analyzing reduced density matrices at different stages of a quantum algorithm's execution and…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
Algorithms for simulating complex physical systems or solving difficult optimization problems often resort to an annealing process. Rather than simulating the system at the temperature of interest, an annealing algorithm starts at a…
We consider an ensemble of $2\times 2$ normal matrices with complex entries representing operators in the quantum mechanics of 2 - level parity-time reversal (PT) symmetric systems. The randomness of the ensemble is endowed by obtaining…
Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for generating unbiased and independent samples from graphical models remains an active research…
Convex regression is a promising area for bridging statistical estimation and deterministic convex optimization. New piecewise linear convex regression methods are fast and scalable, but can have instability when used to approximate…
Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous…
Spectra of ordered eigenvalues of finite Random Matrices are interpreted as a time series. Dataadaptive techniques from signal analysis are applied to decompose the spectrum in clearly differentiated trend and fluctuation modes, avoiding…
The application of random-matrix theory (RMT) to compound-nucleus (CN) reactions is reviewed. An introduction into the basic concepts of nuclear scattering theory is followed by a survey of phenomenological approaches to CN scattering. The…
We apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q < 1. We obtain analytical…
Ensembles of networks arise in various fields where multiple independent networks are observed on the same set of nodes, for example, a collection of brain networks constructed on the same brain regions for different individuals. However,…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
This article is an introductory review of random matrix theory (RMT) and its applications, with special focus on quantum chaos. Random matrices were first used by Wigner to understand the spectra of complex nuclei from a statistical…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…