Spatio-temporal structure of correlations and optimal forecasts of future correlations is a task of major importance. However, the information about cross-correlations and their temporal dynamics is usually inferred from historical (past) observations, which are inevitably contaminated by measurement noise and it is a constant challenge to unscramble signal from noise. The main purpose of this thesis is to study the dynamical properties of real complex systems such as e.g. economy and/or financial market by looking at their spectral properties eg. density of eigenvalues under umbrella of Free Random Variables Calculus and Random Matrix Theory.

1. POSTER: Applying Free Random Variables to the Analysis of Temporal Correlations in Real Complex Systems, PDF document, version 1.4, 0.2MB

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