Even if all the zombies do is walk toward you, they will win if they are uniformly distributed and know where you are. Common sense says that you do not walk toward a potential infinity of zombies, each of whom can sense you. If they have nonzero speed, they will converge toward you.

Lets assume zombies know less about pursuit curves than I do, but that they know some geometry as well as being able to determine your velocity. If they are uniformly distributed in a region which excludes a radial section no bigger than 2 arctan(mu/nu), they either follow you or go at a constant rate normal to and intercepting your path. Since there are infinitely many of them, they will have enough time for one of them to reach you. If the radial arc is larger, head down the middle, don't stop, and don't slow down.

Even if all the zombies do is walk toward you, they will win if they are uniformly distributed and know where you are. Common sense says that you do not walk toward a potential infinity of zombies, each of whom can sense you. If they have nonzero speed, they will converge toward you.

Lets assume zombies know less about pursuit curves than I do, but that they know some geometry as well as being able to determine your velocity. If they are uniformly distributed in a region which excludes a radial section no bigger than 2 arctan(mu/nu) (Edit, I mean 2arctan nu: mu is not a velocity of you) they either follow you or go at a constant rate normal to and intercepting your path. Since there are infinitely many of them, they will have enough time for one of them to reach you. If the radial arc is larger, head down the middle, don't stop, and don't slow down.