Tail and moment estimates for some types of chaos

Let X-i be a sequence of independent symmetric real random variables with l ogarithmically concave tails. We consider a variable X = Sigma(i not equal j) a(i,j)X(i).X-j, where a(i,j) are real numbers. We derive approximate for mulas for the tails and moments of X and of its decoupled version, which ar e exact up to some universal constants.