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Título: A Proof Of Alon's Second Eigenvalue Conjecture And Related Problems | |
| Autor: Friedman Joel | Precio: $787.40 | |
| Editorial: American Mathematical Society | Año: 2008 | |
| Tema: Matematicas, Problemas | Edición: 1ª | |
| Sinopsis | ISBN: 9780821842805 | |
| A d-regular graph has largest or first (adjacency matrix) eigenvalue \lambda 1=d. Consider for an even \ge 4, a random d-regular graph model formed from d/2 uniform, independent permutations on \{1,\ldots,n\}. The author shows that for any \epsilon>0 all eigenvalues aside from \lambda 1=d are bounded by 2\sqrt{d-1}\;+\epsilon with probability 1-O(n{-\tau}), where \tau=\lceil \bigl(\sqrt{d-1}\;+1\bigr)/2 \rceil-1. He also shows that this probability is at most $1-c/n{\tau'}, for a constant c and a \tau' that is either \tau or \tau+1 ("more often" \tau than \tau+1). He proves related theorems for other models of random graphs, including models with d odd. | ||
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