I've heard a lot about multiverse from pop science TV shows and lectures. Somehow, physicists are very good at philosophizing their own theories and coming up with catchy terms that stem imagination of the public.
However, it seems to me that what physicists call "multiverse" is the same with mathematicians' "realization" in probability. Am I wrong about this?
The multiverse as a concept in mathematics can be seen in set theory. It is essentially a view about models of set theory. It acknowledges the existence of vary valid set theory models but no absolute or, roughly put, "true" models.
I will refer you to Antos et al paper Multiverse conceptions in set theory.
J. D. Hamkins' The set-theoretic multiverse might also be of interest.
Regarding your specific question, I would be more careful when calling it a "realization". In probability, and mathematics in general, definitions are very important and they help mathematicians all over the World be consistent and come to a consensus. I would explore these two references first.