Sparse sampling and dilation operations on a Gibbs weighted tree, and multifractal formalism
Abstract
In this article, starting from a Gibbs capacity, we build a new random capacity by applying two simple operators, the first one introducing some redundancy and the second one performing a random sampling. Depending on the values of the two parameters ruling the redundancy and the sampling, the new capacity has very different multifractal behaviors. In particular, the multifractal spectrum of the capacity may contain two to four phase transitions, and the multifractal formalism may hold only on a strict subset (sometimes, reduced to a single point) of the spectrum's domain.
Keywords
Cite
@article{arxiv.2304.11250,
title = {Sparse sampling and dilation operations on a Gibbs weighted tree, and multifractal formalism},
author = {Julien Barral and Stéphane Seuret},
journal= {arXiv preprint arXiv:2304.11250},
year = {2023}
}
Comments
31 pages, 5 figures; the statement of Theorem 2.5 has been simplified with new equivalent definitions of some parameters and is now easier to compare to those of Theorems 2.1 and 2.4. Also, the statements of Theorems 4.7 and 5.9 are more precise