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We show that an infinite weighted tree admits a bi-Lipschitz embedding into Hilbert space if and only if it does not contain arbitrarily large complete binary trees with uniformly bounded distortion.
Martingales with values in uniformly convex spaces
G. Pisier · 1975
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On the moduli of convexity and smoothness
T. Figiel · 1976
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Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach
B. Maurey and G. Pisier · 1976
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On infinite-dimensional topological groups
P. Enflo · 1978
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Classical Banach spaces. II
J. Lindenstrauss and L. Tzafriri · 1979
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Filling Riemannian manifolds
M. Gromov · 1983
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Random walks on discrete groups: boundary and entropy
V. A. Kaĭmanovich and A. M. Vershik · 1983
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Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: a note on combinatorial properties of metric spaces
A. W. M. Dress · 1984
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Long range estimates for Markov chains
N. T. Varopoulos · 1985
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The metrical interpretation of superreflexivity in Banach spaces
J. Bourgain · 1986
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On type of metric spaces
J. Bourgain, V. Milman, and H. Wolfson · 1986
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Probabilistic methods in the geometry of Banach spaces
G. Pisier · 1986
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Extension of Lipschitz mappings on metric trees
J. Matoušek · 1990
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Markov chains, Riesz transforms and Lipschitz maps
K. Ball · 1992
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Isoperimetric inequalities and transient random walks on graphs
C. Thomassen · 1992
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Sharp uniform convexity and smoothness inequalities for trace norms
K. Ball, E. A. Carlen, and E. H. Lieb · 1994
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The geometry of graphs and some of its algorithmic applications
N. Linial, E. London, and Y. Rabinovich · 1995
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Random walks on the lamplighter group
R. Lyons, R. Pemantle, and Y. Peres · 1996
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Remarks on non linear type and Pisier’s inequality
A. Naor and G. Schechtman · 2002
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On hypersphericity of manifolds with finite asymptotic dimension
A. N. Dranishnikov · 2003
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A tight bound on approximating arbitrary metrics by tree metrics
J. Fakcharoenphol, S. Rao, and K. Talwar · 2003
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Markov processes and Ramsey theory for trees
H. Furstenberg and B. Weiss · 2003
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Bounded geometries, fractals, and low-distortion embeddings
A. Gupta, R. Krauthgamer, and J. R. Lee · 2003
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Bi-Lipschitz embeddings of trees into Euclidean buildings
E. Leuzinger · 2003
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Every graph with a positive Cheeger constant contains a tree with a positive Cheeger constant
I. Benjamini and O. Schramm · 1997
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Low distortion Euclidean embeddings of trees
N. Linial, A. Magen, and M. E. Saks · 1998
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On approximating arbitrary metrices by tree metrics
Y. Bartal · 1999
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On embedding trees into uniformly convex Banach spaces
J. Matoušek · 1999
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Steiner points in tree metrics don’t (really) help
A. Gupta · 2001
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Lipschitz quotients from metric trees and from Banach spaces containing l 1 l_{1}
W. B. Johnson, J. Lindenstrauss, D. Preiss, and G. Schechtman · 2002
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The Euclidean distortion of complete binary trees
N. Linial and M. Saks · 2003
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Low-distortion embeddings of general metrics into the line
M. Bădoiu, J. Chuzhoy, P. Indyk, and A. Sidiropoulos · 2005
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Embedding of hyperbolic spaces in the product of trees
S. Buyalo and V. Schroeder · 2005
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Nagata dimension, quasisymmetric embeddings, and Lipschitz extensions
U. Lang and T. Schlichenmaier · 2005
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Metric cotype
M. Mendel and A. Naor · 2005
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Markov chains in smooth Banach spaces and Gromov hyperbolic metric spaces
A. Naor, Y. Peres, O. Schramm, and S. Sheffield · 2006
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