Central limit theorems under special relativity

Ian W. McKeague

Statistics & Probability Letters, 2015, vol. 99, issue C, 149-155

Abstract: Several relativistic extensions of the Maxwell–Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.

Keywords: Heavy-tailed distributions; Random walks on locally compact Lie groups; κ-deformations; Maxwell–Boltzmann; Ornstein–Uhlenbeck (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2014.12.028

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