Vectorial Multifractal Measures: Theories and Applications to Branching Random Walks

Name: Vectorial Multifractal Measures: Theories and Applications to Branching Random Walks
Brand: Springer
SKU: 9783032200648
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by Najmeddine Attia , Amal Mahjoub

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ISBN13: 9783032200648
Binding: Paperback
Subject: N/A
Publisher: Springer
Publisher Imprint: Springer
Publication Date: April 23, 2026
Pages: 137
Original Price: EUR 54.49
Language: English
Edition: N/A
Item Weight: 210 grams
BISAC Subject(s): Mathematical Analysis

About The Book

This book introduces a new multifractal vectorial formalism based on Hewitt-Stromberg measures, with particular emphasis on its application to branching random walks on the Galton-Watson tree. This formalism relies on the use of vector-valued functions defined on balls in a metric space and taking values in a Banach space, thus offering a generalization of classical multifractal analysis. These measures lie between Hausdorff and packing measures and then, the authors' study is specially imported especially when the classical multifractal formalism does not hold. The authors investigate the fractal dimension of the sets of infinite branches of the boundary of a super-critical Galton-Watson tree (endowed with a random metric) along which the averages of a valued branching random walk, have a given set of limit points.

Furthermore, the authors examine additional general sets of levels in multifractal analysis, leading to the development of a relative multifractal vectorial formalism. They explore this relative formalism within the framework of the branching random walk.

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