A strong law of large numbers for iterated functions of independent random variables

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Abstract

We study sequences of random variables obtained by iterative procedures, which can be thought of as nonlinear generalizations of the arithmetic mean. We prove a strong law of large numbers for a class of such iterations. This gives rise to the concept of generalized expected value of a random variable, for which we prove an analog of the classical Jensen inequality. We give several applications to models arising in mathematical physics and other areas.

Original languageEnglish (US)
Pages (from-to)1373-1384
Number of pages12
JournalJournal of Statistical Physics
Volume86
Issue number5-6
DOIs
StatePublished - Mar 1997

Keywords

  • Disordered systems
  • Hierarchical models
  • Law of large numbers
  • Martingales
  • Self-averaging

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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