Nonextensive and superstatistical generalizations of random-matrix theory

Abstract

Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented other versions of the theory that keep base invariance on the expense of allowing correlations between matrix elements. This is achieved by starting from non-extensive entropies rather than the standard Shannon entropy, or following the basic prescription of the recently suggested concept of superstatistics. We review these generalizations of RMT and illustrate their value by calculating the nearest-neighbor-spacing distributions and comparing the results of calculation with experiments and numerical-experiments on systems in transition from order to chaos.

25 pages, 2 figures

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Cited by in corpus (7)

• Theoretical foundations and mathematical formalism of the power-law tailed statistical distributions
• Maximum entropy principle and power-law tailed distributions
• Generalized statistical mechanics for superstatistical systems
• Physical origin of the power-law tailed statistical distributions
• Relativistic Roots of $\kappa$-Entropy
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• Power-Law tailed statistical distributions and Lorentz transformations