Statistics of the eigenvalues of Tsallis matrices

Fernando D Nobre and Andre M.C Souza

Physica A: Statistical Mechanics and its Applications, 2004, vol. 339, issue 3, 354-368

Abstract: The statistics of the eigenvalues of symmetric random matrices, composed by real and statistically independent elements following the distribution that maximizes Tsallis's entropy, is carried numerically in the limit of large matrices. For entropic indexes in the interval −∞2. The density of eigenvalues appears to be symmetric around zero, exhibiting a peak at the origin that becomes steeper for increasing values of q, approaching a delta function at the origin when q→3. The distribution of level spacings displays a form that resembles the well-known Wigner's surmise (augmented by a long tail) for q slightly greater than 53, but gets deformed for increasing values of q, approaching an exponential decay for q>2. For q close to 3, our results resemble those of very sparse random matrices (characterized by many zero matrix elements).

Keywords: Random matrices; Nonextensive statistical mechanics; Tsallis's distributions; Lévy flights (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:339:y:2004:i:3:p:354-368

DOI: 10.1016/j.physa.2004.03.069

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