More air in the world

As I sit here, taking up space, it occurs to me that when a person dies, when they're gone and buried or cremated, the air molecules must rush in to fill the void. Does that make the air thinner? Or does the fact that there's one less person breathing in, and out, somehow thicken our soupy atmosphere? Or, like so many things, does it all balance and out and actually, when someone dies, it makes no difference at all? I wonder.