The spectral dimension of generic trees

Journal article

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, defined as the exponential decay rate of the two-point function along the spine, is 1/3.

Authors: Durhuus, B; Jonsson, T; Wheater, J

• Publication status: Published
• Journal: JOURNAL OF STATISTICAL PHYSICS
• Volume: 128
• Issue: 5
• Pages: 1237-1260
• Publication date: 2006-07-11
• DOI: 10.1007/s10955-007-9348-3
• EISSN: 1572-9613
• ISSN: 0022-4715
• Keywords: math.MP; math.PR; math-ph; hep-th