The Spectral Dimension of Generic Trees
The Spectral Dimension of Generic Trees
复制标题
通用树的谱维
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
J. Wheater
中科院分区：
文献类型：
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作者：
B. Durhuus;T. Jonsson;J. Wheater
摘要
我们定义了无限树的通用系综。这些极限是固定大小N的有限树的集合的N→∞极限，用一组分支权定义。在这些合奏是那些支持树的顶点一致有界的顺序。相关的概率测度支持在具有单个脊柱和Hausdorff维数dh=2的树上。我们的主要结果是，系综平均的谱维数为ds=4/3，和临界指数的质量，定义为指数衰减率的两点函数沿着脊柱，是1/3。
Abstract
We define generic ensembles of infinite trees. These are limits as N→∞ 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 dh=2. Our main result is that the spectral dimension of the ensemble average is ds=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.