|author:||Loh, Po-Shen and Schulman, Leonard J.|
|title:||Improved Expansion of Random Cayley Graphs|
|keywords:||expander graphs, Cayley graphs, second eigenvalue, logarithmic generators|
|abstract:||In Random Cayley Graphs and Expanders, N. Alon and Y. Roichman proved that for every ε > 0
there is a finite c(ε) such that for any
sufficiently large group G, the expected value of the
second largest (in absolute value) eigenvalue of the normalized
adjacency matrix of the Cayley graph with respect to
c(ε) log |G| random elements is less than
ε. We reduce the number of elements to
c(ε)log D(G) (for the same c),
where D(G) is the sum of the dimensions of the
irreducible representations of G. In sufficiently
non-abelian families of groups (as measured by these dimensions), log D(G) is asymptotically (1/2)log|G|. As is well known, a small eigenvalue implies large graph expansion (and conversely); see Tanner84 and AlonMilman84-2,AlonMilman84-1. For any specified eigenvalue or expansion, therefore, random Cayley graphs (of sufficiently non-abelian groups) require only half as many edges as was previously known.
If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files.
|reference:||Loh, Po-Shen and Schulman, Leonard J. (2004), Improved Expansion of Random Cayley Graphs, Discrete Mathematics and Theoretical Computer Science 6, pp. 523-528|
|bibtex:||For a corresponding BibTeX entry, please consider our BibTeX-file.|
|ps.gz-source:||dm060222.ps.gz (35 K)|
|ps-source:||dm060222.ps (87 K)|
|pdf-source:||dm060222.pdf (67 K)|
The first source gives you the `gzipped' PostScript, the second the plain PostScript and the third the format for the Adobe accrobat reader. Depending on the installation of your web browser, at least one of these should (after some amount of time) pop up a window for you that shows the full article. If this is not the case, you should contact your system administrator to install your browser correctly.
Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.