It probably takes some time if they are sending invite emails individually, although I would guess that if it's w the same professor, the initial round of invites would prob all come on the same day. For most schools it definitely depends on which adviser you were applying to work with - at my school, my adviser always sent out acceptance calls (not emails) within 1-3 days after interviews, but other profs in my program took quite a bit longer. Also, even if you're applying to work w the same prof, if one person is wait-listed you might get an acceptance call a few to several weeks later if someone who was given an offer declines. That happened to one of my friends in grad school with me - I got an offer the next day; my friend was waitlisted and got an offer a few weeks later with the same lab/prof.