If $Q_n=X_nM_nX_n=\sum_{i,j=1}^n X_i m_{nij}X_j$, $X_n=(X_1,...,X_n)$ where $X_j$ are iid random variables and $M_n=(m_{nij})$ is a symmetric matrix with extending rownumber in $n\to\infty$.
Iam looking for assertions to clarify in which cases there exists a limit-distribution for $Q_n$?
E.g. there is a quadratic form which has the same trace for all n.