Central limit theorems for nonlinear hierarchical sequences of random variables

Jan Wehr, Jung M. Woo

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5 Scopus citations

Abstract

Let a random variable x0 and a function f: [a, b]k → [a, b] be given. A hierarchical sequence {xn: n = 0, 1, 2,...} of random variables is defined inductively by the relation xn = f(xn-1, 1, xn-1, 2...., xn-1 k), where {xn-1, i: i = 1, 2,..., k} is a family of independent random variables with the same distribution as xn-1. We prove a central limit theorem for this hierarchical sequence of random variables when a function f satisfies a certain averaging condition. As a corollary under a natural assumption we prove a central limit theorem for a suitably normalized sequence of conductivities of a random resistor network on a hierarchical lattice.

Original languageEnglish (US)
Pages (from-to)777-797
Number of pages21
JournalJournal of Statistical Physics
Volume104
Issue number3-4
DOIs
StatePublished - Aug 1 2001

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Keywords

  • Central limit theorem
  • Hierarchical lattices
  • Random resistor networks
  • Renormalization group

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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