Reasoning out the empirical rule d ̃ < 2

Kumiko Hattori, Tetsuya Hattori, Hiroshi Watanabe

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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 languageEnglish
Pages (from-to)207-212
Number of pages6
JournalPhysics Letters A
Issue number5
Publication statusPublished - 1986 Apr 14
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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