# distribution of the coordinates of the second eigenvalues of a large d-regular graph

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)?

Does anyone know some advances on this problem?

• The title is incomprehensible. You want the coordinate of the second eigenvector, and what paper are you referring to? – Igor Rivin Aug 16 '12 at 21:21
• cleaned up formatting and retagged. I too find the combination of question and title hard to follow. – Yemon Choi Aug 16 '12 at 21:46