Structure of spanning trees on the two-dimensional Sierpinski gasket
arXiv:0806.0721
Abstract
Consider spanning trees on the two-dimensional Sierpinski gasket SG(n) where stage is a non-negative integer. For any given vertex of SG(n), we derive rigorously the probability distribution of the degree at the vertex and its value in the infinite limit. Adding up such probabilities of all the vertices divided by the number of vertices, we obtain the average probability distribution of the degree . The corresponding limiting distribution gives the average probability that a vertex is connected by 1, 2, 3 or 4 bond(s) among all the spanning tree configurations. They are rational numbers given as , , , .
32 pages, 5 figures, 1 table