Central Limit Theorems under additive deformations

Daniel J. Eck, Ian W. McKeague

Research output: Contribution to journalArticlepeer-review


Additive deformations of statistical systems arise in various areas of physics. Classical central limit theory is then no longer applicable, even when standard independence assumptions are preserved. This paper investigates ways in which deformed algebraic operations lead to distinctive central limit theory. We establish some general central limit results that are applicable to a range of examples arising in nonextensive statistical mechanics, including the addition of momenta and velocities via Kaniadakis addition, and Tsallis addition. We also investigate extensions to random additive deformations, and find evidence (based on simulation studies) for a universal limit specific to each statistical system.

Original languageEnglish (US)
Pages (from-to)156-162
Number of pages7
JournalStatistics and Probability Letters
StatePublished - Nov 1 2016
Externally publishedYes


  • Kaniadakis addition
  • Probability on Lie groups
  • Tsallis entropy

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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