Fluctuations of extensive functions of quenched random couplings

Jan Wehr, Michael Aizenman

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Abstract

An extensive quantity is a family of functions Ψv of random parameters, indexed by the finite regions V (subsets of ℤd) over which Ψv are additive up to corrections satisfying the boundary estimate stated below. It is shown that unless the randomness is nonessential, in the sense that lim Ψv/|V| has a unique value in the absolute (i.e., not just probabilistic) sense, the variance of such a quantity grows as the volume of V. Of particular interest is the free energy of a system with random couplings; for such Ψv bounds are derived also for the generating function E(e). In a separate application, variance bounds are used for an inequality concerning the characteristic exponents of directed polymers in a random environment.

Original languageEnglish (US)
Pages (from-to)287-306
Number of pages20
JournalJournal of Statistical Physics
Volume60
Issue number3-4
DOIs
Publication statusPublished - Aug 1990
Externally publishedYes

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Keywords

  • directed polymers
  • extensive quantities
  • fluctuations
  • Random systems
  • static disorder

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

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