Random Matrix Theory and a Definition of Correlations in Financial Markets

Korotkikh, Galina

doi:10.1007/978-1-4757-5226-7_11

Cited by 1 publication

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“…Usually, in space and time information about a complex system is given by time series that can be used to characterize correlations through the variance-covariance matrix. Based on computational results [7], [16], [17] we suggest to apply eigenvalues and eigenvectors of variancecovariance matrices to obtain information about a complex system in the hierarchical network from the information about the system in space and time. In particular, this could specify the correlation structure and the geometrical pattern of the Earth system by using corresponding time series.…”

Section: The Hierarchical Network Of Prime Integer Relations As a Pos...mentioning

confidence: 99%

From Space and Time to a Deeper Reality as a Possible Way to Solve Global Problems

Korotkikh,

Korotkikh

2011

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To deal with global problems we suggest to consider complex systems not in space and time, but in a possible deeper reality, i.e., the hierarchical network of prime integer relations. Encoded by arithmetic through the self-organization processes the hierarchical network appears as the mathematical structure of one harmonious and interconnected whole. Remarkably, the holistic nature of the hierarchical network allows to formulate a single universal objective of a complex system defined in terms of the integration principle. We propose that by the realization of the integration principle the Earth system could be transformed to become an integrated part of a larger system with more capacity and energy to sustain life. Significantly, based on integers and controlled by arithmetic only the hierarchical network has a unique potential to provide an irreducible common ground fully trusted by different parties and helping to reveal a higher collective purpose.

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Section: The Hierarchical Network Of Prime Integer Relations As a Pos...mentioning

confidence: 99%