On the Aldous-Caputo Spectral Gap Conjecture for Hypergraphs

Gil Alon; Gady Kozma; Doron Puder

doi:10.1017/S0305004125000179

On the Aldous-Caputo Spectral Gap Conjecture for Hypergraphs

Gil Alon, Gady Kozma, Doron Puder

Mathematics

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

Abstract

In their celebrated paper [CLR10], Caputo, Liggett and Richthammer proved Aldous’ conjecture and showed that for an arbitrary finite graph, the spectral gap of the interchange process is equal to the spectral gap of the underlying random walk. A crucial ingredient in the proof was the Octopus Inequality — a certain inequality of operators in the group ring R ^`Sym_n of the symmetric group. Here we generalise the Octopus Inequality and apply it to generalising the Caputo–Liggett–Richthammer Theorem to certain hypergraphs, proving some cases of a conjecture of Caputo.

Original language	English
Pages (from-to)	259-298
Number of pages	40
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	179
Issue number	2
DOIs	https://doi.org/10.1017/S0305004125000179
State	Published - 21 May 2025

Bibliographical note

Publisher Copyright:
©C The Author(s), 2025. Published by Cambridge University Press on behalf of Cambridge Philosophical Society.

Access to Document

10.1017/S0305004125000179

Cite this

@article{54b7c33b79bd40bc81d0a9abab1202b5,

title = "On the Aldous-Caputo Spectral Gap Conjecture for Hypergraphs",

abstract = "In their celebrated paper [CLR10], Caputo, Liggett and Richthammer proved Aldous{\textquoteright} conjecture and showed that for an arbitrary finite graph, the spectral gap of the interchange process is equal to the spectral gap of the underlying random walk. A crucial ingredient in the proof was the Octopus Inequality — a certain inequality of operators in the group ring R `Symn of the symmetric group. Here we generalise the Octopus Inequality and apply it to generalising the Caputo–Liggett–Richthammer Theorem to certain hypergraphs, proving some cases of a conjecture of Caputo.",

author = "Gil Alon and Gady Kozma and Doron Puder",

note = "Publisher Copyright: {\textcopyright}C The Author(s), 2025. Published by Cambridge University Press on behalf of Cambridge Philosophical Society.",

year = "2025",

month = may,

day = "21",

doi = "10.1017/S0305004125000179",

language = "אנגלית",

volume = "179",

pages = "259--298",

journal = "Mathematical Proceedings of the Cambridge Philosophical Society",

issn = "0305-0041",

publisher = "Cambridge University Press",

number = "2",

}

TY - JOUR

T1 - On the Aldous-Caputo Spectral Gap Conjecture for Hypergraphs

AU - Alon, Gil

AU - Kozma, Gady

AU - Puder, Doron

PY - 2025/5/21

Y1 - 2025/5/21

N2 - In their celebrated paper [CLR10], Caputo, Liggett and Richthammer proved Aldous’ conjecture and showed that for an arbitrary finite graph, the spectral gap of the interchange process is equal to the spectral gap of the underlying random walk. A crucial ingredient in the proof was the Octopus Inequality — a certain inequality of operators in the group ring R `Symn of the symmetric group. Here we generalise the Octopus Inequality and apply it to generalising the Caputo–Liggett–Richthammer Theorem to certain hypergraphs, proving some cases of a conjecture of Caputo.

AB - In their celebrated paper [CLR10], Caputo, Liggett and Richthammer proved Aldous’ conjecture and showed that for an arbitrary finite graph, the spectral gap of the interchange process is equal to the spectral gap of the underlying random walk. A crucial ingredient in the proof was the Octopus Inequality — a certain inequality of operators in the group ring R `Symn of the symmetric group. Here we generalise the Octopus Inequality and apply it to generalising the Caputo–Liggett–Richthammer Theorem to certain hypergraphs, proving some cases of a conjecture of Caputo.

UR - https://www.scopus.com/pages/publications/105005879617

U2 - 10.1017/S0305004125000179

DO - 10.1017/S0305004125000179

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:105005879617

SN - 0305-0041

VL - 179

SP - 259

EP - 298

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 2

ER -

On the Aldous-Caputo Spectral Gap Conjecture for Hypergraphs

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this