Exact multifractal spectra for arbitrary Laplacian random walks
Exact multifractal spectra for arbitrary Laplacian random walks
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DOI：
10.1103/physrevlett.88.055506
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发表时间：
2002-02-04
影响因子：
8.6
通讯作者：
Hastings, MB
中科院分区：
文献类型：
--
作者：
Hastings, MB
利用迭代保角映射得到了二维任意拉普拉斯随机游走的谐波测度的精确多重分形谱。分离的光谱被发现用来描述生长测量在时间上的标度，生长尖端附近的标度，以及远离生长尖端的标度。远离尖端的光谱与中心电荷c小于或等于1的共形不变平衡系统的光谱一致，而c与所选择的特定行走有关，而平衡性质不能从时间和尖端附近得到标度。
Iterated conformal mappings are used to obtain exact multifractal spectra of the harmonic measure for arbitrary Laplacian random walks in two dimensions. Separate spectra are found to describe scaling of the growth measure in time, of the measure near the growth tip, anal of the measure away from the growth tip. The spectra away from the tip coincide with those of conformally invariant equilibrium systems with arbitrary central charge c less than or equal to 1, with c related to the particular walk chosen, while the scaling in time and near the tip cannot be obtained from the equilibrium properties.