Is there a version of the Gärtner-Ellis Theorem that can deal with matrices? And if there is, do you know where I can find it? Thank you for your help!
My problem is that I have a sequence of matrices of random variables that are not independent. I want to make a statement about the asymptotical probability that these matrices exceed a certain threshold. I would prefer using some Large Deviations result like Gärtner-Ellis so if anyone knows anything, I'd be happy to hear it!