Spectral analysis of finite-time correlation matrices near equilibrium phase transitions

Understand

We study spectral densities for systems on lattices, which, at a phase transition display, power-law spatial correlations.

• Constructing the spatial correlation matrix we prove that its eigenvalue density shows a power law that can be derived from the spatial correlations.
• In practice time series are short in the sense that they are either not stationary over long time intervals or not available over long time intervals.
• Also we usually do not have time series for all variables available.