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- W2283491695 abstract "Cawley and Mauldin analyzed multifractal structure of a probability measure (an invari- ant measure) ρ induced on a Moran fractal. They introduced a system of weights as well as the probability measure and gave an example in which the multifractal structure presents spin-glass features and showed the gauge invariance. In this paper, we consider the invariant set obtained by a random iteraition algorithm. This random algorithm introduces the assoiated pobability and weight. The multifractal de- compositions of the set with respect to the pair of probability density and weight density are considered. To characterize the the Hausdorff dimension of the decomposed sets, we introduce a pair of parameters (q, s). Using these parameters we represent the formula of the Hausdorff dimension. This extension of introducing a pair of parameters gives us the freedom to in- vestigate the spinglass phenomena of mutifractal structure. Furthermore we show the gauge invariance holds." @default.
- W2283491695 created "2016-06-24" @default.
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- W2283491695 date "2014-03-01" @default.
- W2283491695 modified "2023-09-23" @default.
- W2283491695 title "Spin-glass Theory of Random Iteration Algorithm" @default.
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- W2283491695 hasPublicationYear "2014" @default.
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