A Proof of Alon's Second Eigenvalue Conjecture and Related Problems Paperback / softback
by Joel Friedman
Part of the Memoirs of the American Mathematical Society series
Paperback / softback
Description
A $d$-regular graph has largest or first (adjacency matrix) eigenvalue $\lambda 1=d$.
Consider for an even $d\ge 4$, 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.
Information
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Item not Available
- Format:Paperback / softback
- Pages:100 pages
- Publisher:American Mathematical Society
- Publication Date:01/01/2008
- Category:
- ISBN:9780821842805
Other Formats
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Information
-
Item not Available
- Format:Paperback / softback
- Pages:100 pages
- Publisher:American Mathematical Society
- Publication Date:01/01/2008
- Category:
- ISBN:9780821842805
