How to handle a schizophrenic coworker that makes me uncomfortable

So I’m a cashier in retail and there’s a new guy hire here and we are a pretty small place so there’s only 4 other full time employees. He’s only been working for a couple days but I’ve noticed he full on talks to himself and laughs at his own conversations he has with himself.

I don’t have any problem with schizophrenic people but it does make me uncomfortable him having a whole conversation with the voices in his head and he keeps hovering around my register trying to ask me personal questions. Hell constantly try to touch my personal belongings when I’m away from my register for a couple times it’s unnerving.

If I talk to another person he repeats back what I said to himself. I’ve brought it up with management and don’t really know how to go about this. I don’t want to be mean but I feel very uncomfortable around him because he does stare at me something a dirty look then says he was just thinking. I don’t think he’s on medication or anything. And am kinda at my wits end honestly even thought it’s only been three days.