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Central limit theorems under special relativity.

Ian W McKeague1

  • 1Department of Biostatistics, Columbia University.

Statistics & Probability Letters
|March 24, 2015
PubMed
Summary
This summary is machine-generated.

This study extends classical central limit theorems under special relativity to explain lognormal tail behavior in astrophysical flux distributions, a phenomenon not explained by existing relativistic Maxwell-Boltzmann distributions.

Keywords:
BoltzmannMaxwellOrnsteinUhlenbeckheavy-tailed distributionsrandom walks on locally compact Lie groupsκ-deformations

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Area of Science:

  • Astrophysics
  • Statistical Mechanics
  • Relativistic Physics

Background:

  • Existing relativistic extensions of the Maxwell-Boltzmann distribution fail to account for observed lognormal tail behavior in astrophysical source flux distributions.
  • The lognormal tail behavior is a significant unexplained feature in various astrophysical phenomena.

Purpose of the Study:

  • To develop extensions of classical central limit theorems under the conditions of special relativity.
  • To provide a theoretical framework that explains the lognormal tail behavior observed in astrophysical flux distributions.

Main Methods:

  • Development of extensions to classical central limit theorems incorporating special relativistic conditions.
  • Analysis of asymptotic distributions within the framework of special relativity.

Main Results:

  • The developed relativistic central limit theorems yield an explicit form for the asymptotic distribution.
  • This explicit form clearly demonstrates lognormal tail behavior, consistent with astrophysical observations.

Conclusions:

  • The novel relativistic central limit theorems offer a theoretical explanation for the lognormal tail behavior in astrophysical flux distributions.
  • This work bridges concepts from special relativity, statistical mechanics, and group theory (CLTs on Lie groups).