TY - JOUR
T1 - Reasoning out the empirical rule d ̃ < 2
AU - Hattori, Kumiko
AU - Hattori, Tetsuya
AU - Watanabe, Hiroshi
PY - 1986/4/14
Y1 - 1986/4/14
N2 - 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.
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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U2 - 10.1016/0375-9601(86)90466-4
DO - 10.1016/0375-9601(86)90466-4
M3 - Article
AN - SCOPUS:0001548482
VL - 115
SP - 207
EP - 212
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
SN - 0375-9601
IS - 5
ER -