Does randomness in multifractals imply latent dimensions?
摘要
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.
引用
@article{arxiv.cond-mat/0401048,
title = {Does randomness in multifractals imply latent dimensions?},
author = {Wei-Xing Zhou and Zun-Hong Yu},
journal= {arXiv preprint arXiv:cond-mat/0401048},
year = {2007}
}
备注
This is a full version of a poster in the 7th International multidisciplinary Conference 17 - 20 March 2002, Granada, Spain. This work was done when I was at ECUST