This is an erratum for paper "Convergence in law in the second Wiener/Wigner chaos" appeared in ECP volume 17 paper number 36.

Let L be the class of limiting laws associated with sequences in the second Wiener chaos. We exhibit a large subset $L_0$ of $L$ satisfying that, for any $F_\infty$ in $L_0$, the convergence of only a finite number of cumulants…