A proof of Alon's second eigenvalue conjecture and related problems
| dc.creator | Friedman, Joel | |
| dc.date | 2004-05-05 | |
| dc.date.accessioned | 2026-07-07T03:21:12Z | |
| dc.date.available | 2026-07-07T03:21:12Z | |
| dc.description | In 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.description | To appear in Memoirs of the American Mathematical Society. 118 pages. This newer version should have a two page glossary | |
| dc.identifier | https://arxiv.org/abs/cs/0405020 | |
| dc.identifier | http://arxiv.org/abs/cs/0405020 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/32109 | |
| dc.subject | Discrete Mathematics | |
| dc.subject | Combinatorics | |
| dc.subject | G.2.2 | |
| dc.title | A proof of Alon's second eigenvalue conjecture and related problems | |
| dc.type | text |