Related papers: Toy Model for Large Non-Symmetric Random Matrices
We study the numerical simulation of supersymmetric models having a local Nicolai map. The mapping can be regarded as a stochastic equation and its numerical integration provides an algorithm for the simulation of the original model. In…
We study the statistical mechanics of classical and quantum systems in non-equilibrium steady states. Emphasis is placed on systems in strong thermal gradients. Various measures and functional forms of observables are presented. The quantum…
This thesis reviews recent progress on products of random matrices from the perspective of exactly solved Gaussian random matrix models. We derive exact formulae for the correlation functions for the eigen- and singular values at arbitrary…
We investigate the joint convergence of independent random Toeplitz matrices with complex input entries that have a pair-correlation structure, along with deterministic Toeplitz matrices and the backward identity permutation matrix.…
We consider a complex-valued linear mixture model, under discrete weakly stationary processes. We recover latent components of interest, which have undergone a linear mixing. We study asymptotic properties of a classical unmixing estimator,…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
This contribution to the proceedings of the Cracow meeting on `Applications of Random Matrix Theory' summarizes a series of studies, some old and others more recent on financial applications of Random Matrix Theory (RMT). We first review…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
In repeated-game applications where both the collusive and non-collusive outcomes can be supported as equilibria, researchers must resolve underlying selection questions if theory will be used to understand counterfactual policies. One…
We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…
Alignment algorithms usually rely on simplified models of gaps for computational efficiency. Based on an isomorphism between alignments and physical helix-coil models, we show in statistical mechanics that alignments with realistic laws for…
We consider in the paper some consequences of the nonsymmetric Kaluza-Klein (Jordan-Thiry) theory with spontaneous symmetry breaking connecting to the existence of the warp factor and communnication in extra-dimensions. We consider a toy…
This work proposes a method to evaluate synthetic tabular data generated to augment small sample datasets. While data augmentation techniques can increase sample counts for machine learning applications, traditional validation approaches…
Synchronized measurements of a large power grid enable an unprecedented opportunity to study the spatialtemporal correlations. Statistical analytics for those massive datasets start with high-dimensional data matrices. Uncertainty is…
Multivariate Distributions are needed to capture the correlation structure of complex systems. In previous works, we developed a Random Matrix Model for such correlated multivariate joint probability density functions that accounts for the…
Statistical static timing analysis deals with the increasing variations in manufacturing processes to reduce the pessimism in the worst case timing analysis. Because of the correlation between delays of circuit components, timing model…
Equilibrium Statistical Mechanics is undoubtedly a cornerstone for the description of many particle systems. The common interpretation is based on ensemble theory as put forward by Gibbs, alongside the basic assumptions that different…
It is shown that the correlation functions of the random variables $\det(\lambda - X)$, in which $X$ is a real symmetric $ N\times N$ random matrix, exhibit universal local statistics in the large $N$ limit. The derivation relies on an…
The generation of synthetic data is an essential tool to study complex systems, allowing for example to test models of these in precisely controlled settings, or to parametrize simulation models when data is missing. This paper focuses on…
Financial markets are prominent examples for highly non-stationary systems. Sample averaged observables such as variances and correlation coefficients strongly depend on the time window in which they are evaluated. This implies severe…