A Proof Of Alon S Second Eigenvalue Conjecture And Related Problems
Download A Proof Of Alon S Second Eigenvalue Conjecture And Related Problems PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get A Proof Of Alon S Second Eigenvalue Conjecture And Related Problems book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
A Proof of Alon's Second Eigenvalue Conjecture and Related Problems
Author: Joel Friedman
language: en
Publisher: American Mathematical Soc.
Release Date: 2008
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.
Sum Formula for SL$_2$ over a Totally Real Number Field
Author: Roelof W. Bruggeman
language: en
Publisher: American Mathematical Soc.
Release Date: 2009-01-21
The authors prove a general form of the sum formula $\mathrm{SL}_2$ over a totally real number field. This formula relates sums of Kloosterman sums to products of Fourier coefficients of automorphic representations. The authors give two versions: the spectral sum formula (in short: sum formula) and the Kloosterman sum formula. They have the independent test function in the spectral term, in the sum of Kloosterman sums, respectively.
Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models
Several types of differential equations, such as delay differential equations, age-structure models in population dynamics, evolution equations with boundary conditions, can be written as semilinear Cauchy problems with an operator which is not densely defined in its domain. The goal of this paper is to develop a center manifold theory for semilinear Cauchy problems with non-dense domain. Using Liapunov-Perron method and following the techniques of Vanderbauwhede et al. in treating infinite dimensional systems, the authors study the existence and smoothness of center manifolds for semilinear Cauchy problems with non-dense domain. As an application, they use the center manifold theorem to establish a Hopf bifurcation theorem for age structured models.