Theoretical physics, sure, ok. Not experimental physics though.

That too. Statistics used to analyze results and turn them into conclusions.

As my mathematical statistics professor told us on the first day, “statistics is not mathematics.” It’s a good idea to remember: if a branch of the subject x is called “mathematical x,” then x in general is not totally mathematical and can be studied to some extent without mathematics.

That's arguable.

The empirical part is not mathematical, in that you run experiments and get results.