Related papers: Asymmetric random matrices: What do we need them f…
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…
Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…
Correlation matrices contain a wide variety of spatio-temporal information about a dynamical system. Predicting correlation matrices from partial time series information of a few nodes characterizes the spatio-temporal dynamics of the…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an…
Financial markets are highly correlated systems that reveal both the inter-market dependencies and the correlations among their different components. Standard analyzing techniques include correlation coefficients for pairs of signals and…
Random correlation matrices are studied for both theoretical interestingness and importance for applications. The author of [6] is interested in their interpretation as covariance matrices of purely random signals, the authors of [16]…
We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems. An oft-encountered problem in computational finance is the…
We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from QCD to high-T_c materials. Instead of working from specific models, phase…
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
Co-occurrence matrices, such as co-citation, co-word, and co-link matrices, have been used widely in the information sciences. However, confusion and controversy have hindered the proper statistical analysis of this data. The underlying…
Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path…
These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition…
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
In this paper, a time series model with coefficients that take values from random matrix ensembles is proposed. Formal definitions, theoretical solutions, and statistical properties are derived. Estimation and forecast methodologies for…
Cross-Correlation random matrices have emerged as a promising indicator of phase transitions in spin systems. The core concept is that the evolution of magnetization encapsulates thermodynamic information [R. da Silva, Int. J. Mod. Phys. C,…