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Sparse sampling and dilation operations on a Gibbs weighted tree, and multifractal formalism

Year: 2023
Type: preprint
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.
DOI: 10.48550/arxiv.2304.11250
Institutions: Centre National de la Recherche Scientifique, Université Sorbonne Paris Nord, Laboratoire Analyse, Géométrie et Applications, Université Paris-Est Créteil, Laboratoire d’Analyse et de Mathématiques Appliquées, Université Gustave Eiffel
Language: English
Open Access status: green
OpenAlex ID: W4366999275
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