Cops never showed up, at least not yet. Might be that they will show up later, I dunno.

In the meantime, however, I've contacted management over this situation. The guy downstairs has done this twice so far, banging on the ceiling when I'm just sitting around and not making any noise. Also, he constantly slams doors, which of course not only causes lots of noise but also makes my entire apartment shake. They said they'll be sending him a letter. I hope that this means that things will get better, though he might decide to retaliate, but in the end I don't know what will happen.