I have raised this sort of question before but I think that now I've found a better term for the subject, one which might ring more bells for people - hence the repost. Hope you won't be too angry with me.

I am interested in eigenvector localization for deterministic matrices. There is a whole body of work on the random matrix setup but I am interested in bounding the ratio between eigenvector coordinates of certain fixed and messy matrices. Any results out there that you know of pertaining to this? (I know the old masters' work on positive/nonnegative matrices but need to handle further cases).