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We describe a natural topological generalization of edge expansion for graphs to regular CW complexes and prove that this property holds with high probability for certain random complexes.
A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations
H. Chernoff · 1952
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On random graphs. I
P. Erdős and A. Rényi · 1959
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On the complexity of a concentrator
M. Pinsker · 1973
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Difference equations, isoperimetric inequality and transience of certain random walks
J. Dodziuk · 1984
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λ 1 \lambda_{1} , isoperimetric inequalities for graphs, and superconcentrators
N. Alon and V.D. Milman · 1985
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Eigenvalues and expanders
N. Alon · 1986
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Ramanujan graphs
A. Lubotzky, R. Phillips, and P. Sarnak · 1988
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Explicit group-theoretic constructions of combinatorial schemes and their applications in the construction of expanders and concentrators
G.A. Margulis · 1988
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Models of random regular graphs
N. C. Wormald · 1999
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Random graphs
Béla Bollobás · 2001
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Ramanujan hypergraphs
W.-C. W. Li · 2004
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Explicit constructions of Ramanujan complexes of type
A. Lubotzky, B. Samuels, and U. Vishne · 2005
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Ramanujan complexes of typeà d
A. Lubotzky, B. Samuels, and U. Vishne · 2005
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Expander graphs and their applications
Shlomo Hoory, Nathan Linial, and Avi Wigderson · 2006
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Homological connectivity of random 2-complexes
N. Linial and R. Meshulam · 2006
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The isoperimetric constant of the random graph process
Itai Benjamini, Simi Haber, Michael Krivelevich, and Eyal Lubetzky · 2008
Vanishing of the top homology of a random complex
L. Aronshtam, N. Linial, T. Luczak, and R. Meshulam · 2010
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Overlap properties of geometric expanders
J. Fox, M. Gromov, V. Lafforgue, A. Naor, and J. Pach · 2010
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Singularities, Expanders and Topology of Maps. Part 2: from Combinatorics to Topology Via Algebraic Isoperimetry
M. Gromov · 2010
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The threshold function for vanishing of the top homology group of random d d -complexes
D.N. Kozlov · 2010
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The fundamental group of random 2-complexes
Eric Babson, Christopher Hoffman, and Matthew Kahle · 2011
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Concentration of measure for the analysis of randomized algorithms
D. Dubhashi and A. Panconesi · 2009
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Homological connectivity of random k-dimensional complexes
R. Meshulam and N. Wallach · 2009
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D. Dotterrer · 2011
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Minors in random and expanding hypergraphs
U. Wagner · 2011
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On Gromov’s Method of Selecting Heavily Covered Points
U. Wagner and J. Matoušek · 2011
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