Related papers: Random Matrix Model for Eigenvalue Statistics in R…
We define a message-passing algorithm for computing magnetizations in Restricted Boltzmann machines, which are Ising models on bipartite graphs introduced as neural network models for probability distributions over spin configurations. To…
Recent works have established a novel viewpoint that treats the eigenvalue spectra of disordered quantum systems as time-series, and corresponding algorithms such as singular-value-decomposition has proven its advantage in studying subtle…
Maximum eigenvalue detection (MED) is an important application of random matrix theory in spectrum sensing and signal detection. However, in small signal-to-noise ratio environment, the maximum eigenvalue of the representative signal is at…
The sub-ohmic spin-boson model is known to possess a novel quantum phase transition at zero temperature between a localised and delocalised phase. We present here an analytical theory based on a variational ansatz for the ground state,…
Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…
Mixed state ensembles such as the Bures-Hall and Hilbert-Schmidt measure are probability distributions that characterise the statistical properties of random density matrices and can be used to determine the typical features of mixed…
Using a new approximate strong-randomness renormalization group (RG), we study the many-body localized (MBL) phase and phase transition in one-dimensional quantum systems with short-range interactions and quenched disorder. Our RG is built…
Power systems are developing very fast nowadays, both in size and in complexity; this situation is a challenge for Early Event Detection (EED). This paper proposes a data- driven unsupervised learning method to handle this challenge.…
Covariance matrices estimated from short, noisy, and non-Gaussian financial time series are notoriously unstable. Empirical evidence suggests that such covariance structures often exhibit power-law scaling, reflecting complex, hierarchical…
The Eigenstate Thermalization Hypothesis explains thermalization in isolated quantum systems through the statistical properties of observables in the energy eigenbasis. We investigate the crossover from integrability to chaos in the…
We provide a pedagogical review on the calculation of highly excited eigenstates of disordered interacting quantum systems which can undergo a many-body localization (MBL) transition, using shift-invert exact diagonalization. We also…
Motivation: In systems biology, modelling strategies aim to decode how molecular components interact to generate dynamical behaviour. Boolean modelling is more and more used, but the description of the dynamics from two-levels components…
We discuss an application of the random matrix theory in the context of estimating the bipartite entanglement of a quantum system. We discuss how the Wishart ensemble (the earliest studied random matrix ensemble) appears in this quantum…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
The random matrix ensembles (RME) of Hamiltonian matrices, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applicable to following quantum statistical systems: nuclear systems, molecular…
We analyze cross-correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of…
In this paper we construct a class of random matrix ensembles labelled by a real parameter $\alpha \in (0,1)$, whose eigenvalue density near zero behaves like $|x|^\alpha$. The eigenvalue spacing near zero scales like $1/N^{1/(1+\alpha)}$…
We report the study of a model of a two-level system interacting in a non-diagonal way with a complex environment described by Gaussian orthogonal random matrices (GORM). The effect of the interaction on the total spectrum and its…
We establish a general framework to explore parametric statistics of individual energy levels in unitary random matrix ensembles. For a generic confinement potential $W(H)$, we (i) find the joint distribution functions of the eigenvalues of…
The dynamical phase diagram of interacting disordered systems has seen substantial revision over the past few years. Theory must now account for a large prethermal many-body localized (MBL) regime in which thermalization is extremely slow,…