Spectrum and combinatorics of two-dimensional Ramanujan complexes

Konstantin Golubev; Ori Parzanchevski

doi:10.1007/s11856-019-1828-z

Spectrum and combinatorics of two-dimensional Ramanujan complexes

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Abstract

Ramanujan graphs have extremal spectral properties, which imply a remarkable combinatorial behavior. In this paper we compute the high dimensional Hodge–Laplace spectrum of Ramanujan triangle complexes, and show that it implies a combinatorial expansion property, and a pseudorandomness result. For this purpose we prove a Cheeger-type inequality and a mixing lemma of independent interest.

Original language	English
Pages (from-to)	583-612
Number of pages	30
Journal	Israel Journal of Mathematics
Volume	230
Issue number	2
DOIs	https://doi.org/10.1007/s11856-019-1828-z
State	Published - 1 Mar 2019
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11856-019-1828-z

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title = "Spectrum and combinatorics of two-dimensional Ramanujan complexes",

abstract = "Ramanujan graphs have extremal spectral properties, which imply a remarkable combinatorial behavior. In this paper we compute the high dimensional Hodge–Laplace spectrum of Ramanujan triangle complexes, and show that it implies a combinatorial expansion property, and a pseudorandomness result. For this purpose we prove a Cheeger-type inequality and a mixing lemma of independent interest.",

author = "Konstantin Golubev and Ori Parzanchevski",

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doi = "10.1007/s11856-019-1828-z",

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AU - Golubev, Konstantin

AU - Parzanchevski, Ori

PY - 2019/3/1

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N2 - Ramanujan graphs have extremal spectral properties, which imply a remarkable combinatorial behavior. In this paper we compute the high dimensional Hodge–Laplace spectrum of Ramanujan triangle complexes, and show that it implies a combinatorial expansion property, and a pseudorandomness result. For this purpose we prove a Cheeger-type inequality and a mixing lemma of independent interest.

AB - Ramanujan graphs have extremal spectral properties, which imply a remarkable combinatorial behavior. In this paper we compute the high dimensional Hodge–Laplace spectrum of Ramanujan triangle complexes, and show that it implies a combinatorial expansion property, and a pseudorandomness result. For this purpose we prove a Cheeger-type inequality and a mixing lemma of independent interest.

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U2 - 10.1007/s11856-019-1828-z

DO - 10.1007/s11856-019-1828-z

M3 - مقالة

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VL - 230

SP - 583

EP - 612

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

ER -

Spectrum and combinatorics of two-dimensional Ramanujan complexes

Abstract

All Science Journal Classification (ASJC) codes

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