Correlations, transitions and early warning signals for non-equilibrium steady or quasi-steady states
by Prof. Thomas H. Seligman (Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México and Centro Internacional de Ciencias Cuernavaca, Morelos, México)
Tuesday, March 14, 2017 from to (Asia/Kolkata)
The spectrum of time series has found successful applications in the understanding of financial markets but has been little used for stochastic dynamical systems. The reason seems to be that most systems studied have a clear spatial structure and many other techniques have been successfully applied. We therefore revisited some well known systems and in particular found analytically that a power law in space implies a power law in the eigenvalues of the correlation spectra . The proof is not invertible and therefore we got interested in analyzing the a case where spatial correlation are known analytically and display no power law, named the totally antisymmetric simple exclusion process (TASEP) . Here we found  a power law for one critical line in parameter space and further interesting deviations from the random matrix behavior, mainly in what is known as the constant current region.  T. Prosen, B. Buča and T.H. Seligman, (2014). Spectral analysis of finite-time correlation matrices near equilibrium phase transitions. EPL (Europhysics Letters), 2015; 108(2), 20006.  Derrida B. Phys. Rep.. 1998; 301(1), 65–83  S. Biswas, F. Leyvraz, P. Monroy Castilero and T.H. Seligman, Sci Rep. 2017; 7: 40506.