Parameswaran Gopikrishnan

TL;DR: In this article, the authors studied the correlation between stock price uctuations of the leading 1000 stocks and showed that the largest 1% of the eigenvalues and corresponding eigenvectors show systematic deviations from the predictions for a random matrix, whereas the rest of the Eigenvalues conform to random matrix behavior.

TL;DR: Methods of random matrix theory (RMT), which originated from the need to understand the interactions between the constituent elements of complex interacting systems, are used to analyze the cross-correlation matrix C of returns, and it is demonstrated that C shares universal properties with the Gaussian orthogonal ensemble of random matrices.

TL;DR: In this article, a heuristic argument that serves to make more plausible the universality hypothesis in both thermal critical phenomena and percolation phenomena was presented, and suggested that this argument could be developed into a possible coherent approach to understand the ubiquity of scale invariance and universality in a wide range of complex systems.

TL;DR: In this article, the authors quantitatively analyze university research activities and compare their growth dynamics with those of business firms, and find that the distribution of growth rates displays a ''universal'' form that does not depend on the size of the university or on the measure of size used, and that the width of this distribution decays with size as a power law.

TL;DR: The analysis of quote data for the 116 most frequently traded stocks on the New York Stock Exchange over the two-year period 1994-1995 shows long-range power-law correlations, similar to those previously found for the volatility, and shows that the bid-ask spread and the volatility are also related logarithmically.