Does randomness in multifractals imply latent dimensions?

Details Does randomness in multifractals imply latent dimensions? Does randomness in multifractals imply latent dimensions?

2004-01-06

arxiv.org/abs/cond-mat/0401048v1

Complexity and Fractals in Nature, M. M. Novok (ed.), 2002, pp. 433-434

Physics

Condensed Matter

Statistical Mechanics

This is a full version of a poster in the 7th International multidisciplinary Conference 17 - 20 March 2002, Granada, Spain. T

Scientific paper

Negative, or latent, dimensions have always attracted a strong interest since their discovery. When randomness is introduced in multifractals, the sample-to-sample fluctuations of multifractal spectra emerge inevitably, which has motivated various studies in this field. In this work, we study a class of multinomial measures and argue the asymptotic behaviors of the multifractal function as . The so-called latent dimensions condition (LDC) is presented which states that latent dimensions may be absent in discrete random multinomial measures. In order to clarify the discovery, several examples are illustrated.

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