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Multifractal spectra of certain random Gibbs measures

Author

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  • Fan, Ai Hua
  • Shieh, Narn-Rueih

Abstract

We consider a random Gibbs measure [mu](d[eta],[omega]) generated by a certain sequence of random functions gn([eta],[omega]) on the configuration space of one-dimensional system of lattice particles. Under concrete conditions, we prove that, for almost sure [omega], [mu](d[eta],[omega]) has a non-random non-trivial multifractal spectrum. The basic idea is to relate our situation to random matrix products discussed in Ruelle (1979, Adv. Math. 32, 68-80).

Suggested Citation

  • Fan, Ai Hua & Shieh, Narn-Rueih, 2000. "Multifractal spectra of certain random Gibbs measures," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 25-31, March.
    • Handle: RePEc:eee:stapro:v:47:y:2000:i:1:p:25-31
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    References listed on IDEAS

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    1. Hu, Xiaoyu & Taylor, S. James, 1997. "The multifractal structure of stable occupation measure," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 283-299, March.
    2. Shieh, Narn-Rueih & Taylor, S. James, 1998. "Logarithmic multifractal spectrum of stable occupation measure," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 249-261, July.
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