相关论文: Finite-Range Coulomb Gas Models I: Some Analytical…

For a large class of quantum systems the statistical properties of their spectrum show remarkable agreement with random matrix predictions. Recent advances show that the scope of random matrix theory is much wider. In this work, we show…

We review a class of matrix models whose degrees of freedom are matrices with anticommuting elements. We discuss the properties of the adjoint fermion one-, two- and gauge invariant D-dimensional matrix models at large-N and compare them…

The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on…

The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…

The strongly coupled lattice gauge models show an interesting mechanism of dynamical mass generation. If a suitable continuum limit can be found, one may think of it as an alternative to the Higgs mechanism. We present data on the spectrum,…

We introduce a power-law banded random matrix model for the third of the three classical Wigner-Dyson ensembles, i.e., the symplectic ensemble. A detailed analysis of the statistical properties of its eigenvectors and eigenvalues, at…

Finite mixtures of regression models offer a flexible framework for investigating heterogeneity in data with functional dependencies. These models can be conveniently used for unsupervised learning on data with clear regression…

The Gray-Scott model is a set of reaction-diffusion equations that describes chemical systems far from equilibrium. Interest in this model stems from its ability to generate spatio-temporal structures, including pulses, spots, stripes, and…

We present an extension of a simple automaton model to incorporate non-local interactions extending over a spatial range in lattice gases. {}From the viewpoint of Statistical Mechanics, the lattice gas with interaction range may serve as a…

The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and…

A simple technique for expanding the free energy of general six-vertex models about free-fermion points is introduced. This technique is used to verify a Coulomb gas prediction about the behavior of the leading singularity in the free…

Random Matrix Theory (RMT) is a powerful statistical tool to model spectral fluctuations. This approach has also found fruitful application in Quantum Chromodynamics (QCD). Importantly, RMT provides very efficient means to separate…

We introduce an equilibrium formulation of the functional renormalization group (fRG) for inhomogeneous systems capable of dealing with spatially finite-ranged interactions. In the general third order truncated form of fRG, the dependence…

We study large fluctuations of the current in a Dyson gas, a 1D system of particles interacting through a logarithmic potential and subjected to random noise. We adapt the macroscopic fluctuation theory to the Dyson gas and derive two…

We consider a system of particles lined up on a finite interval with Coulomb 3-dimensional interactions between close neighbours, i.e. only a few other neighbours apart. This model was introduced by Malyshev (2015) to study the flow of…

For random matrices with block correlation structure we show that the fluctuations of linear eigenvalue statistics are Gaussian on all mesoscopic scales with universal variance which coincides with that of the Gaussian unitary or Gaussian…

We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…

In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null…

Inspired by "quantum graphity" models for spacetime, a statistical model of graphs is proposed to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a very…

In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced by a modified hyperscaling relation. As a result, standard…