Answer:
One of the most common (and frustrating) aspects of the job search process for both me and my candidates is waiting to hear back from firms after a submission or an interview (*especially* an interview). While the information and advice that follows won't necessarily speed up the process of waiting, hopefully knowing the dynamics will make the wait a little easier or less stressful.
The main reason you haven't heard anything right away may seem obvious, but bears repeating because it is often forgotten from the standpoint of the candidate - everyone is very busy!
The recruiting coordinator at the law firm who receives and screens the initial applications is busy - in the current market, it is not uncommon for any given job posting to receive dozens, if not hundreds, of applicants, especially in the larger markets. During certain times of the year, recruiting coordinators may also be inundated with the work surrounding on-campus interviews, coordinating the orientation of new hires, preparing for and networking at industry conventions, etc. They work extremely hard to keep on top of everything, but this often means that it can take a long time for even the most diligent and responsive recruiting coordinator to be in a position to respond to a submission.
