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We initiate the study of Boolean function analysis on high-dimensional expanders.
p p -adic curvature and the cohomology of discrete subgroups of p p -adic groups
1973
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A Krawtchouk polynomial addition theorem and wreath products of symmetric groups
1976
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Ramanujan graphs
1988
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Differential posets
1988
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Variations on differential posets
——— · 1990
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Boolean functions whose Fourier transform is concentrated on the first two levels and neutral social choice
2002
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Rapid mixing of Glauber dynamics up to uniqueness via contraction
——— · 2004
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Ramanujan hypergraphs
2004
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Ramanujan complexes of type A d ~ \tilde{A_{d}}
——— · 2005
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Homological connectivity of random 2-complexes
2006
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Sub-constant error low degree test of almost-linear size
2008
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Singularities, expanders and topology of maps. Part 2: from combinatorics to topology via algebraic isoperimetry
2010
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2010
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KKL, Kruskal-Katona, and monotone nets
2013
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A stability result for balanced dictatorships in S n {S}_{n}
——— · 2015
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Finite quotients of Bruhat–Tits buildings as geometric expanders
2017
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On expansion and topological overlap
2018
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Good distance lattices from high dimensional expanders , 2018
2018
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Pseudorandom sets in Grassmann graph have near-perfect expansion
——— · 2018
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Local spectral expansion approach to high dimensional expanders part I: Descent of spectral gaps
2018
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2016
Cited alongside, same era.
An orthogonal basis for functions over a slice of the Boolean hypercube
——— · 2016
Cited alongside, same era.
Isoperimetric inequalities for ramanujan complexes and topological expanders
2016
Cited alongside, same era.
Low degree Boolean functions on S n {S}_{n} , with an application to isoperimetry
——— · 2017
Cited alongside, same era.
Approximating constraint satisfaction problems on high-dimensional expanders
Cited in the paper.
A matrix trickle-down theorem on simplicial complexes and applications to sampling colorings
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Log-concave polynomials II: high-dimensional walks and an FPRAS for counting bases of a matroid
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2019
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High order random walks: Beyond spectral gap
2020
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