Isoperimetric stability in lattices

Ben Barber; Joshua Erde; Peter Keevash; Alexander Roberts

doi:10.1090/proc/16439

Isoperimetric stability in lattices

Ben Barber, Joshua Erde, Peter Keevash, Alexander Roberts

Institute of Discrete Mathematics (5050)

Research output: Contribution to journal › Article › peer-review

Abstract

We obtain isoperimetric stability theorems for general Cayley digraphs on Zd. For any fixed B that generates Zd over Z, we characterise the approximate structure of large sets A that are approximately isoperimetric in the Cayley digraph of B: we show that A must be close to a set of the form kZ ∩ Zd, where for the vertex boundary Z is the conical hull of B, and for the edge boundary Z is the zonotope generated by B.

Original language	English
Pages (from-to)	5021-5029
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	151
Issue number	12
Early online date	2023
DOIs	https://doi.org/10.1090/proc/16439
Publication status	E-pub ahead of print - 2023

Keywords

Isoperimetry
Stability
Convex Geometry

ASJC Scopus subject areas

Applied Mathematics
Mathematics(all)

Access to Document

10.1090/proc/16439

2007.14457v2Licence: Other

Cite this

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AB - We obtain isoperimetric stability theorems for general Cayley digraphs on Zd. For any fixed B that generates Zd over Z, we characterise the approximate structure of large sets A that are approximately isoperimetric in the Cayley digraph of B: we show that A must be close to a set of the form kZ ∩ Zd, where for the vertex boundary Z is the conical hull of B, and for the edge boundary Z is the zonotope generated by B.

KW - Isoperimetry

KW - Stability

KW - Convex Geometry

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Isoperimetric stability in lattices

Abstract

Keywords

ASJC Scopus subject areas

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