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Multifractal Analysis of Complex Random Cascades

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Abstract

We achieve the multifractal analysis of a class of complex valued statistically self-similar continuous functions. For we use multifractal formalisms associated with pointwise oscillation exponents of all orders. Our study exhibits new phenomena in multifractal analysis of continuous functions. In particular, we find examples of statistically self-similar such functions obeying the multifractal formalism and for which the support of the singularity spectrum is the whole interval [0, ∞].

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Authors and Affiliations

  1. LAGA (UMR 7539), Département de Mathématiques, Institut Galilée, Université Paris 13, 99 avenue Jean-Baptiste Clément, 93430, Villetaneuse, France

    Julien Barral

  2. INRIA Rocquencourt, B.P. 105, 78153, Le Chesnay Cedex, France

    Xiong Jin

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  1. Julien Barral
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  2. Xiong Jin
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Correspondence to Julien Barral.

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Communicated by S. Smirnov

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Barral, J., Jin, X. Multifractal Analysis of Complex Random Cascades. Commun. Math. Phys. 297, 129–168 (2010). https://doi.org/10.1007/s00220-010-1030-y

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