Related papers: Asymmetric random matrices: What do we need them f…

Non-symmetric rectangular correlation matrices occur in many problems in economics. We test the method of extracting statistically meaningful correlations between input and output variables of large dimensionality and build a toy model for…

Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in chemical, ecological, climate, or neural systems. Despite their importance, general mechanisms for their emergence are little understood. In order…

Correlation matrices are a major type of multivariate data. To examine properties of a given correlation matrix, a common practice is to compare the same quantity between the original correlation matrix and reference correlation matrices,…

We present a general class of machine learning algorithms called parametric matrix models. In contrast with most existing machine learning models that imitate the biology of neurons, parametric matrix models use matrix equations that…

We analyze the spectral properties of large, time-lagged correlation matrices using the tools of random matrix theory. We compare predictions of the one-dimensional spectra, based on approaches already proposed in the literature. Employing…

In these lectures we discuss some elementary concepts in connection with the theory of symmetric spaces applied to ensembles of random matrices. We review how the relationship between random matrix theory and symmetric spaces can be used in…

This article discusses how concepts and methods of complex networks can be applied to real-time imaging and computer vision. After a brief introduction of complex networks basic concepts, their use as means to represent and characterize…

This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…

In this work, we present a new approach for constructing models for correlation matrices with a user-defined graphical structure. The graphical structure makes correlation matrices interpretable and avoids the quadratic increase of…

The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…

Using an asymmetric associative network with synchronous updating, it is possible to recall a sequence of patterns. To obtain a stable sequence generation with a large storage capacity, we introduce a threshold that eliminates the…

Moments of secular and inverse secular coefficients, averaged over random matrices from classical groups, are related to the enumeration of non-negative matrices with prescribed row and column sums. Similar random matrix averages are…

We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the…

Inferring causal models from observed correlations is a challenging task, crucial to many areas of science. In order to alleviate the computational effort when sifting through possible causal explanations for some given observations, it is…

We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but general symmetric random matrices are also…

Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations…

Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the…

. The choice of a suitable random matrix model of a complex system is very sensitive to the nature of its complexity. The statistical spectral analysis of various complex systems requires, therefore, a thorough probing of a wide range of…

Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…

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…