Random Vectors and their inner product.

Let's say i have two random vectors, X and Y, both of length n. The elements of either vector are not independent, and X and Y themselves are not independent. All elements are non-negative.

I want to explore the behaviour of the inner product of X and Y as \(n\to\infty\).

Not sure where to begin though: does anyone know of any good references/advice to get me started? Cheers.