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The spectral dimension of generic trees

Abstract:

We define generic ensembles of infinite trees. These are limits as $N\to\infty$ of ensembles of finite trees of fixed size $N$, defined in terms of a set of branching weights. Among these ensembles are those supported on trees with vertices of a uniformly bounded order. The associated probability measures are supported on trees with a single spine and Hausdorff dimension $d_h =2$. Our main result is that their spectral dimension is $d_s=4/3$, and that the critical exponent of the mass, define...

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Publication status:
Published

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Publisher copy:
10.1007/s10955-007-9348-3

Authors


Durhuus, B More by this author
Jonsson, T More by this author
More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Physics, Theoretical Physics
Journal:
JOURNAL OF STATISTICAL PHYSICS
Volume:
128
Issue:
5
Pages:
1237-1260
Publication date:
2006-07-11
DOI:
EISSN:
1572-9613
ISSN:
0022-4715
URN:
uuid:f130a723-b69b-4472-a0c8-e77bf9a33199
Source identifiers:
17394
Local pid:
pubs:17394

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