A Proof of Alon s Second Eigenvalue Conjecture and Related Problems is popular PDF and ePub book, written by Joel Friedman in 2008, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, A Proof of Alon s Second Eigenvalue Conjecture and Related Problems can be Read Online from any device for your convenience.
A Proof of Alon s Second Eigenvalue Conjecture and Related Problems Book PDF Summary
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.
Detail Book of A Proof of Alon s Second Eigenvalue Conjecture and Related Problems PDF
- Author : Joel Friedman
- Release : 20 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821842805
- Genre : Mathematics
- Total Page : 114 pages
- Language : English
- PDF File Size : 16,7 Mb
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