distribution of the coordinates of the second eigenvalues of a large d-regular graph - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T11:29:42Z http://mathoverflow.net/feeds/question/104870 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/104870/distribution-of-the-coordinates-of-the-second-eigenvalues-of-a-large-d-regular-gr distribution of the coordinates of the second eigenvalues of a large d-regular graph pgiacome 2012-08-16T20:52:57Z 2012-10-15T23:22:01Z <p>in the paper "expander graphs with applications" an intriguing problem was posed Fix an integer \$d ≥ 3\$ and consider large random \$(n, d)\$-graphs. What can be said about the distribution of the coordinates of \$v_2\$? Specifically, does \$v_2\$ tend to be uniformly distributed on the unit sphere (in which the distribution of these coordinates is nearly normal)?</p> <p>Does anyone know some advances on this problem?</p> http://mathoverflow.net/questions/104870/distribution-of-the-coordinates-of-the-second-eigenvalues-of-a-large-d-regular-gr/104879#104879 Answer by Igor Rivin for distribution of the coordinates of the second eigenvalues of a large d-regular graph Igor Rivin 2012-08-16T23:29:18Z 2012-08-16T23:29:18Z <p>You might want to check ou<a href="http://arxiv.org/pdf/0910.5306.pdf" rel="nofollow">t this preprint by Dimitriou and Pal</a>, and voluminous references therein.</p>