We've been shown in Game of Thrones that people who die north of The Wall can end up becoming wights (another footman in the army of the dead), and we also know that anyone killed by a White Walker (or in the vicinity of one, by a wight) is also a candidate for joining the army of the dead.
We also know, now (spoilers for S07E06)...
... that the control over a group of wights is localised to individual White Walkers - meaning that killing a White Walker who is magically linked to a group of wights will "de-activate" those wights, leaving them permanently dead (until another White Walker might walk in and revive them with magic again).
Q: Do we know all the possible ways this spell of animating the dead, which has been compared to zombieism, can propagate? Is it possible, for example, for a lone wight in a populated area to make other people wights
(i.e. if a wight kills someone, does that someone become a wight, too, like a zombie? Or do they have to be near a White Walker?)