A stable distribution that is centered and symmetrical has a value $\alpha \leq 1$ the expected value of the distribution is undefined.
I have also been told that if a Levy Flight has it's step lengths drawn from the absolute of the stable distribution it will become superdiffusive when $\alpha = 1$ but not when $2 \geq \alpha > 1$.
Is it true that levy flights would only be superdiffusive when $\alpha \leq 1$ and why is that?