On the Exact Dimension of Mandelbrot Measure

• Autorzy: Attia Najmeddine

Identyfikatory

DOI

10.19195/0208-4147.39.2.4

• Języki publikacji: EN

Abstrakty

EN

We develop, in the context of the boundary of a supercritical Galton-Watson tree, a uniform version of the argument used by Kahane (1987) on homogeneous trees to estimate almost surely and simultaneously the Hausdorff and packing dimensions of the Mandelbrot measure over a suitable set J. As an application, we compute, almost surely and simultaneously, the Hausdorff and packing dimensions of the level sets E(α) of infinite branches of the boundary of the tree along which the averages of the branching random walk have a given limit point.

Słowa kluczowe

EN

Mandelbrot measure; Hausdorff dimension

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2019
• Tom: Vol. 39, Fasc. 2
• Strony: 299--314
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Attia Najmeddine

• Faculté des Sciences de Monastir, Avenue de l’environnement 5000 Monastir, Tunisia

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).