The spectral gap is analyzed in the [foundational paper][1] I don't know if you can say anything else.

<cite authors="Omer Reingold, Salil Vadhan, and Avi Wigderson" mrnumber="1888797" cite="_Ann. of Math. (2)_ **155** (2002), no. 1, 157--187">_Omer Reingold, Salil Vadhan, and Avi Wigderson_, MR 1888797 [**Entropy waves, the zig-zag graph product, and new constant-degree expanders**](http://dx.doi.org/10.2307/3062153), _Ann. of Math. (2)_ **155** (2002), no. 1, 157--187.</cite>
  [1]: http://www.math.ias.edu/~avi/PUBLICATIONS/MYPAPERS/SALIL/EXPANDERS/ANNALS/RVW01.pdf