Spanning trees in two dimensions
作者： S. S. Manna , Deepak Dhar , S. N. Majumdar
DOI: 10.1103/PHYSREVA.46.R4471
关键词: Lattice model (finance) 、 Physics 、 Monte Carlo method 、 Tree (descriptive set theory) 、 Spanning tree 、 Loop (topology) 、 Square lattice 、 Combinatorics 、 Probability distribution 、 Stochastic process
摘要: We describe the results of an analytical and numerical study geometrical properties random spanning trees on a square lattice. determine exactly probability distribution coordination number at site tree. argue that s sites get disconnected from tree deleting bond varies as ${\mathit{s}}^{\mathrm{\ensuremath{-}}11/8}$ for large s. The loop perimeter l is formed adding additional link ${\mathit{l}}^{\mathrm{\ensuremath{-}}8/5}$ l. These distributions are also determined numerically in Monte Carlo simulation generated by using Broder's algorithm. complete agreement with theoretical predictions.
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