A Proof of Alon's Second Eigenvalue Conjecture and Related Problems

A Proof of Alon's Second Eigenvalue Conjecture and Related Problems
Author :
Publisher : American Mathematical Soc.
Total Pages : 114
Release :
ISBN-10 : 9780821842805
ISBN-13 : 0821842803
Rating : 4/5 (803 Downloads)

Book Synopsis A Proof of Alon's Second Eigenvalue Conjecture and Related Problems by : Joel Friedman

Download or read book A Proof of Alon's Second Eigenvalue Conjecture and Related Problems written by Joel Friedman and published by American Mathematical Soc.. This book was released on 2008 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


A Proof of Alon's Second Eigenvalue Conjecture and Related Problems Related Books

A Proof of Alon's Second Eigenvalue Conjecture and Related Problems
Language: en
Pages: 114
Authors: Joel Friedman
Categories: Mathematics
Type: BOOK - Published: 2008 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

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 fro
Sheaves on Graphs, Their Homological Invariants, and a Proof of the Hanna Neumann Conjecture
Language: en
Pages: 124
Authors: Joel Friedman
Categories: Mathematics
Type: BOOK - Published: 2014-12-20 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

In this paper the author establishes some foundations regarding sheaves of vector spaces on graphs and their invariants, such as homology groups and their limit
Analysis and Geometry on Graphs and Manifolds
Language: en
Pages: 493
Authors: Matthias Keller
Categories: Mathematics
Type: BOOK - Published: 2020-08-20 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

This book addresses the interplay between several rapidly expanding areas of mathematics. Suitable for graduate students as well as researchers, it provides sur
Expander Families and Cayley Graphs
Language: en
Pages: 283
Authors: Mike Krebs
Categories: Mathematics
Type: BOOK - Published: 2011-10-21 - Publisher: OUP USA

DOWNLOAD EBOOK

Expander families enjoy a wide range of applications in mathematics and computer science, and their study is a fascinating one in its own right. Expander Famili
Scattering Resonances for Several Small Convex Bodies and the Lax-Phillips Conjecture
Language: en
Pages: 90
Authors: Luchezar N. Stoyanov
Categories: Mathematics
Type: BOOK - Published: 2009 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

This work deals with scattering by obstacles which are finite disjoint unions of strictly convex bodies with smooth boundaries in an odd dimensional Euclidean s