Distributional Limits of Riemannian Manifolds and Graphs with Sublinear Genus Growth
Distributional Limits of Riemannian Manifolds and Graphs with Sublinear Genus Growth
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黎曼流形和次线性亏格增长图的分布极限
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
J. Souto
中科院分区：
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作者：
Hossein Namazi;Pekka Pankka;J. Souto
Benjamini和Schramm在[BS 01]中引入了具有一致有界价的图序列的分布极限的概念，并研究了当所涉及的图是平面图时的分布极限。研究了具有有界曲率的黎曼流形序列满足拟共形条件的分布极限。然后，我们应用我们的结果有所改善Benjamini和Schramm的原始结果的复发的简单随机游动的限制，平面图。例如，作为一个应用，我们给出了一个事实的证明，即在一个扩展家庭的图，每个图的亏格是有界的顶点数的线性函数从下面。
In Benjamini and Schramm [BS01] introduced the notion of distributional limit of a sequence of graphs with uniformly bounded valence and studied such limits in the case that the involved graphs are planar. We investigate distributional limits of sequences of Riemannian manifolds with bounded curvature which satisfy a quasi-conformal condition. We then apply our results to somewhat improve Benjamini’s and Schramm’s original result on the recurrence of the simple random walk on limits of planar graphs. For instance, as an application we give a proof of the fact that for graphs in an expander family, the genus of each graph is bounded from below by a linear function of the number of vertices.