I didn't see anything on the EN FFXIV twitter about this but there appears to be a few posts on the JP twitter talking about alpha invites. I used Google translate.
Dec 3: Done to increase the number of newborn FFXIV α tester, I was sending the winning email! Those who are elected to participate in the test are available immediately. I do not forget to check your e-mails! # FF14
Dec 3: Depending on the rate of future simultaneous connections the way, the next increase in the number α tester is expected to be 12/5. # FF14
Link to the twitter account. https://twitter.com/FF_XIV_JP
Edited, Dec 4th 2012 9:34am by Geffe