Reasoning out the empirical rule d ̃ < 2

Kumiko Hattori; Tetsuya Hattori; Hiroshi Watanabe

doi:10.1016/0375-9601(86)90466-4

Reasoning out the empirical rule d ̃ < 2

Kumiko Hattori, Tetsuya Hattori, Hiroshi Watanabe

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

There is an empirical rule that the exactly evaluated spectral dimensions ( d ̃) of finitely ramified fractals obey d ̃ < 2. We prove this rule under general assumptions. For this purpose, we define d ̃ rigorously in terms of field theory on networks, and then look into the dynamics of random walks.

Original language	English
Pages (from-to)	207-212
Number of pages	6
Journal	Physics Letters A
Volume	115
Issue number	5
DOIs	https://doi.org/10.1016/0375-9601(86)90466-4
Publication status	Published - 1986 Apr 14
Externally published	Yes

ASJC Scopus subject areas

Physics and Astronomy(all)

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10.1016/0375-9601(86)90466-4

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abstract = "There is an empirical rule that the exactly evaluated spectral dimensions ( d{\~ }) of finitely ramified fractals obey d{\~ } < 2. We prove this rule under general assumptions. For this purpose, we define d{\~ } rigorously in terms of field theory on networks, and then look into the dynamics of random walks.",

author = "Kumiko Hattori and Tetsuya Hattori and Hiroshi Watanabe",

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AU - Watanabe, Hiroshi

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AB - There is an empirical rule that the exactly evaluated spectral dimensions ( d ̃) of finitely ramified fractals obey d ̃ < 2. We prove this rule under general assumptions. For this purpose, we define d ̃ rigorously in terms of field theory on networks, and then look into the dynamics of random walks.

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Reasoning out the empirical rule d ̃ < 2

Abstract

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