Related papers: Matrix Models of Strength Distributions
Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition…
Load models have a great impact on voltage behaviors as well as power system transient dynamics. Extensive work has been done on this topic, proposing appropriate load models and capturing better load behaviors during transient. This paper…
It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic fields with special symmetries. In particular, flux lines…
A connection between integrability properties and general statistical properties of the spectra of symmetric transfer matrices of the asymmetric eight-vertex model is studied using random matrix theory (eigenvalue spacing distribution and…
In this article we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy-level distribution of a fractal follows a power-law behaviour, if its energy spectrum is a limit set of piece-wise…
The problem of distributed matrix multiplication with straggler tolerance over finite fields is considered, focusing on field sizes for which previous solutions were not applicable (for instance, the field of two elements). We employ…
We introduce a new random matrix model called distance covariance matrix in this paper, whose normalized trace is equivalent to the distance covariance. We first derive a deterministic limit for the eigenvalue distribution of the distance…
This paper focuses on cascading line failures in the transmission system of the power grid. Recent large-scale power outages demonstrated the limitations of percolation- and epid- emic-based tools in modeling cascades. Hence, we study…
Situations in many fields of research, such as digital communications, nuclear physics and mathematical finance, can be modelled with random matrices. When the matrices get large, free probability theory is an invaluable tool for describing…
In this article, we study the Faraday effect in a binary composite consisting of a dielectric matrix with metallic inclusions. We first use the replica trick together with a variational method in order to compute the effective permittivity…
A transverse multipole expansion is derived, including the longitudinal components necessarily present in regions of varying magnetic field profile. It can be used for exact numerical orbit following through the fringe field regions of…
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…
Three-way data can be conveniently modelled by using matrix variate distributions. Although there has been a lot of work for the matrix variate normal distribution, there is little work in the area of matrix skew distributions. Three matrix…
Neural network models are one of the most successful approaches to machine learning, enjoying an enormous amount of development and research over recent years and finding concrete real-world applications in almost any conceivable area of…
MDPs with low-rank transitions -- that is, the transition matrix can be factored into the product of two matrices, left and right -- is a highly representative structure that enables tractable learning. The left matrix enables expressive…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
In the limit of vanishing lattice spacing we provide a rigorous variational coarse-graining result for a next-to-nearest neighbor lattice model of a simple crystal. We show that the $\Gamma$-limit of suitable scaled versions of the model…
We consider a flat lattice of dipoles modeled by harmonic oscillators interacting with the electromagnetic field in dipole approximation. Eliminating the variables from the coupled equations of motion, we come to effective Maxwell…
We investigate phase transitions in three dimensional scalar matrix models, with special emphasis on complex $2 \times 2$ matrices. The universal equation of state for weak first order phase transitions is computed. We also study the coarse…
Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the…