Random groups and property (T ): Żuk's theorem revisited

Autor:	Michał Kotowski, Marcin Kotowski
Rok vydání:	2013
Předmět:	Discrete mathematics Random group Property (philosophy) General Mathematics 20F65 Mathematics - Group Theory Mathematics
Zdroj:	Journal of the London Mathematical Society. 88:396-416
ISSN:	0024-6107
DOI:	10.1112/jlms/jdt024
Popis:	We provide a full and rigorous proof of a theorem attributed to \.Zuk, stating that random groups in the Gromov density model for d > 1/3 have property (T) with high probability. The original paper had numerous gaps, in particular, crucial steps involving passing between different models of random groups were not described. We fix the gaps using combinatorial arguments and a recent result concerning perfect matchings in random hypergraphs. We also provide an alternative proof, avoiding combinatorial difficulties and relying solely on spectral properties of random graphs in G(n, p) model. Comment: v2: minor corrections
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3a23f6bb374edc294d0e7a9939baa2bb https://doi.org/10.1112/jlms/jdt024 Zobrazit plný text záznamu Plný text