Multifractal spectra of certain random Gibbs measures

Ai Hua Fan and Narn-Rueih Shieh

Statistics & Probability Letters, 2000, vol. 47, issue 1, 25-31

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).

Keywords: Gibbs; measure; Pressure; function; Multifractal; spectrum (search for similar items in EconPapers)
Date: 2000
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