We analyse the eigenvalue fluctuations of the Laplacian of various networks under the random matrix theory framework. Analyses of random networks, scale-free networks and small-world networks show that the nearest neighbor spacing distribution of the Laplacian of these networks follow Gaussian...

We revisit the index leverage effect, that can be decomposed into a volatility effect and a correlation effect. We investigate the latter using a matrix regression analysis, that we call ‘Principal Regression Analysis’ (PRA) and for which we provide some analytical (using Random Matrix...

We investigated the topological properties of stock networks constructed by a minimal spanning tree. We compared the original stock network with the estimated network; the original network is obtained by the actual stock returns, while the estimated network is the correlation matrix created by...

We discuss the statistics of long queues, in which the interdeparture time statistics is dominated by spatial interactions among the elements in a queue rather than the arrival or exit processes. Based on a Fokker–Planck approach, it is possible to calculate the stationary distance...

A financial market is an example of an adaptive complex network consisting of many interacting units. This network reflects market’s behavior. In this paper, we use Random Matrix Theory (RMT) notion for specifying the largest eigenvector of correlation matrix as the market mode of stock...

Two aspects of noncolliding diffusion processes have been extensively studied. One of them is the fact that they are realized as harmonic Doob transforms of absorbing particle systems in the Weyl chambers. Another aspect is integrability in the sense that any spatio-temporal correlation function...

We perform a rather careful spectral analysis of the correlation structures observed in real and financial returns for a large pool of long-lived US corporations, and find that financial returns are characterized by strong collective fluctuations that are absent from real returns. Once the...

We analyze protein–protein interaction networks for six different species under the framework of random matrix theory. Nearest neighbor spacing distribution of the eigenvalues of adjacency matrices of the largest connected part of these networks emulate universal Gaussian orthogonal statistics...

Let (εj)j≥0 be a sequence of independent p-dimensional random vectors and τ≥1 a given integer. From a sample ε1,…,εT+τ of the sequence, the so-called lag-τ auto-covariance matrix is Cτ=T−1∑j=1Tετ+jεjt. When the dimension p is large compared to the sample size T, this paper...

The aim of this paper is to show that random matrix theory (RMT) can be a useful addition to the economist?s tool-kit in the analysis of macro-economic time series data. A great deal of applied economic work relies upon empirical estimates of the correlation matrix. However due to the finite...