Universal distribution from magnetic nanograins to financial markets in terms of random matrix theorem

Random matrix theory is an essential scheme to analyze data from basic science to financial markets. Having a mesoscopic nanoball formed by a few hundred atoms, the distribution of the eigenenergies of the grain Hamiltonian agrees with the prediction of random matrix theorem (if they structural disordered), in agreement with the experimental findings [1]. The case of Au nanoballs is a sterling example to introduce the topic, which guides us to novel results in magnetism. We examine the distribution of the magnetic anisotropy (MA) of d1 impurities embedded into Au nanograins. The MA can be characterized by five real parameters, and the radial distribution in this parameter space is found as a universal when the structural disorder is large enough, see the attached figure, and implies rise to anomalies in the specific heat, susceptibility and excitation spectra [2]. However, we show that the random matrix approach is also used to describe phenomena in social science or finance, e.g. the dynamics of stock inventory variations [3].



[1] F. Kuemmeth, K. I. Bolotin, S. Shi and D. C. Ralph, Nano Lett., 8 4506-4512, (2008).

[2] A. Szilva, P. Balla, O. Eriksson, G. Zaránd, and L. Szunyogh, Phys. Rev. B (2015) (accepted).

[3] W.-X. Zhou, G.-H. Mu, J. Kertész, New J. Phys. 14, 093025, (2012)