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We present an elementary way to transform an expander graph into a simplicial complex where all high order random walks have a constant spectral gap, i.e., they converge rapidly to the stationary distribution.
Über teiler, faktoren und charakteristische polynome von graphen
Horst Sachs · 1966
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Spectra of Cayley graphs
László Babai · 1979
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Ramanujan graphs
Alexander Lubotzky, Ralph Phillips, and Peter Sarnak · 1988
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Michael Sipser and Daniel A Spielman · 1994
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Entropy waves, the zig-zag graph product, and new constant-degree expanders
Omer Reingold, Salil Vadhan, and Avi Wigderson · 2002
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A proof of Alon’s second eigenvalue conjecture
Joel Friedman · 2003
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Elementary bounds on Poincaré and log-Sobolev constants for decomposable Markov chains
Mark Jerrum, Jung-Bae Son, Prasad Tetali, Eric Vigoda, et al · 2004
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Explicit constructions of Ramanujan complexes of type Ad
Alexander Lubotzky, Beth Samuels, and Uzi Vishne · 2005
Earlier work this paper cites.
Expander graphs and their applications
Shlomo Hoory, Nathan Linial, and Avi Wigderson · 2006
Cited alongside, same era.
Homological connectivity of random 2-complexes
Nathan Linial and Roy Meshulam · 2006
Cited alongside, same era.
Singularities, expanders and topology of maps. Part 2: From combinatorics to topology via algebraic isoperimetry
Mikhail Gromov · 2010
Cited alongside, same era.
A combinatorial construction of almost-ramanujan graphs using the zig-zag product
Avraham Ben-Aroya and Amnon Ta-Shma · 2011
Cited alongside, same era.
Lectures on mixing times
Nathanaël Berestycki · 2014
Cited alongside, same era.
Ramanujan complexes and bounded degree topological expanders
Tali Kaufman, David Kazhdan, and Alexander Lubotzky · 2014
Cited alongside, same era.
High dimensional expanders imply agreement expanders
Irit Dinur and Tali Kaufman · 2017
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High order random walks: Beyond spectral gap
Tali Kaufman and Izhar Oppenheim · 2017
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Markov chains and mixing times
David A Levin and Yuval Peres · 2017
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Alexander Lubotzky · 2017
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Expander Graphs–Both Local and Global
Michael Chapman, Nati Linial, and Yuval Peled · 2018
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Bounded degree cosystolic expanders of every dimension
Shai Evra and Tali Kaufman · 2016
Cited alongside, same era.
High dimensional random walks and colorful expansion
Tali Kaufman and David Mass · 2016
Cited alongside, same era.
Nima Anari, Kuikui Liu, Shayan Oveis Gharan, and Cynthia Vinzant · 2019
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Construction of new local spectral high dimensional expanders
Tali Kaufman and Izhar Oppenheim · 2019
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