A proof of Alon's second eigenvalue conjecture and related problems

dc.creatorFriedman, Joel
dc.date2004-05-05
dc.date.accessioned2026-07-07T03:21:12Z
dc.date.available2026-07-07T03:21:12Z
dc.descriptionIn this paper we show the following conjecture of Noga Alon. Fix a positive integer d>2 and real epsilon > 0; consider the probability that a random d-regular graph on n vertices has the second eigenvalue of its adjacency matrix greater than 2 sqrt(d-1) + epsilon; then this probability goes to zero as n tends to infinity. We prove the conjecture for a number of notions of random d-regular graph, including models for d odd. We also estimate the aforementioned probability more precisely, showing in many cases and models (but not all) that it decays like a polynomial in 1/n.
dc.descriptionTo appear in Memoirs of the American Mathematical Society. 118 pages. This newer version should have a two page glossary
dc.identifierhttps://arxiv.org/abs/cs/0405020
dc.identifierhttp://arxiv.org/abs/cs/0405020
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/32109
dc.subjectDiscrete Mathematics
dc.subjectCombinatorics
dc.subjectG.2.2
dc.titleA proof of Alon's second eigenvalue conjecture and related problems
dc.typetext

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