TY - JOUR
T1 - On the Aldous-Caputo Spectral Gap Conjecture for Hypergraphs
AU - Alon, Gil
AU - Kozma, Gady
AU - Puder, Doron
N1 - Publisher Copyright:
©C The Author(s), 2025. Published by Cambridge University Press on behalf of Cambridge Philosophical Society.
PY - 2025/9/1
Y1 - 2025/9/1
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
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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 -