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Spectral Dimension of Trees with a Unique Infinite Spine

Abstract:

Using generating functions techniques we develop a relation between the Hausdorff and spectral dimension of trees with a unique infinite spine. Furthermore, it is shown that if the outgrowths along the spine are independent and identically distributed, then both the Hausdorff and spectral dimension can easily be determined from the probability generating function of the random variable describing the size of the outgrowths at a given vertex, provided that the probability of the height of the ...

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Publisher copy:
10.1007/s10955-012-0510-1

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Journal:
Journal of Statistical Physics
Volume:
147
Issue:
5
Pages:
942-962
Publication date:
2012-06-05
DOI:
ISSN:
0022-4715
URN:
uuid:acaa1d04-785d-4833-a7df-dfca5c72a12b
Source identifiers:
341582
Local pid:
pubs:341582

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