I have the following problem : I have $X_1, \dots, X_n$, $n$ i.i.d. random variables in $\mathbb{R}^p$. They are bounded, but I think that it is not important. I also have an embedding map $f : \mathbb{R}^p \rightarrow \mathbb{R}^q$ that has a bounded image. I think that this hypothesis is much more important.
I am looking at concentration inequalities of the matrix $((f(X_i) - E(f(X_i))^T(f(X_j) - E(f(X_j)))_{i, j}$ around its expectation, if possible in terms of operator norm.
In particular, it is easily seen that this expectation is the diagonal matrix with the variances of the $f(X_i)$'s on the diagonal.
I no not know where to start. Regular concentration inequalities that typically require independence do not apply here.
Thanks in advance.