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?

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

You might want to check out this preprint by Dimitriou and Pal, and voluminous references therein.

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