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Displaying similar documents to “On the sphericity of scaling limits of random planar quadrangulations.”

Helly Property for Subtrees

Jessica Enright, Piotr Rudnicki (2008)

Formalized Mathematics

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We prove, following [5, p. 92], that any family of subtrees of a finite tree satisfies the Helly property.MML identifier: HELLY, version: 7.8.09 4.97.1001

The maximum multiplicity and the two largest multiplicities of eigenvalues in a Hermitian matrix whose graph is a tree

Rosário Fernandes (2015)

Special Matrices

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The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree, M1, was understood fully (froma combinatorial perspective) by C.R. Johnson, A. Leal-Duarte (Linear Algebra and Multilinear Algebra 46 (1999) 139-144). Among the possible multiplicity lists for the eigenvalues of Hermitian matrices whose graph is a tree, we focus upon M2, the maximum value of the sum of the two largest multiplicities when the largest multiplicity is M1. Upper and lower bounds are given for M2....

Metric Characterizations of Superreflexivity in Terms of Word Hyperbolic Groups and Finite Graphs

Mikhail Ostrovskii (2014)

Analysis and Geometry in Metric Spaces

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We show that superreflexivity can be characterized in terms of bilipschitz embeddability of word hyperbolic groups.We compare characterizations of superrefiexivity in terms of diamond graphs and binary trees.We show that there exist sequences of series-parallel graphs of increasing topological complexitywhich admit uniformly bilipschitz embeddings into a Hilbert space, and thus do not characterize superrefiexivity.

Inverse Limit Spaces Satisfying a Poincaré Inequality

Jeff Cheeger, Bruce Kleiner (2015)

Analysis and Geometry in Metric Spaces

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We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [12]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of examples for which our conditions are satisfied. Included are known examples of PI spaces, such as...