Harmonic trees
نویسندگان
چکیده
منابع مشابه
On Harmonic Functions on Trees
By a tree T we mean a connected graph such that every subgraph obtained from T by removing any of its edges is not connected. In what follows we will only consider trees in which we distinguish a vertex v0 as an origin. As usual we denote by V and E the set of vertices and the set of edges (respectively) of the tree. If v and w are the boundary vertices of an edge, we say that they are neighbou...
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The harmonic index H (G) of a graph G is defined as the sum of the weights 2 du+dv of all edges uv of G, where du denotes the degree of a vertex u in G. In this paper, we determine (i) the trees of order n and m pendant vertices with the second smallest harmonic index, (ii) the trees of order n and diameter r with the smallest and the second smallest harmonic indices, and (iii) the trees of ord...
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(1) In Section 2, we define the notion of harmonic maps and quadratic differentials. Then we give a harmonic map proof of Teichmuller’s theorem by Wolf. (See [2], [9]) (2) In Section 3, we explain a compactification of Teichmuller spaces by Wolf using harmonic maps. (See [2], [4], [10], [11]) (3) In Section 4, we review the Morgan-Shalen compactification and the Korevaar-Schoen limit. Then we g...
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We study properties of the harmonic measure of balls in typical large discrete trees. For a ball of radius n centered at the root, we prove that, although the size of the boundary is of order n, most of the harmonic measure is supported on a boundary set of size approximately equal to n , where β ≈ 0.78 is a universal constant. To derive such results, we interpret harmonic measure as the exit d...
متن کاملHausdorff Dimension of the Harmonic Measure on Trees
For a large class of Markov operators on trees we prove the formula HD = h=l connecting the Hausdorr dimension of the harmonic measure on the tree boundary, the rate of escape l and the asymptotic entropy h. Applications of this formula include random walks on free groups, conditional random walks, random walks in random environment and random walks on treed equivalence relations. 0. Introducti...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2002
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(02)00076-9