Lifschitz tail and sausage asymptotics for stable processes in the Poissonian environment on the Sierpinski gasket

We obtain the Lifschitz tail asymptotics for the integrated density of states of the subordinate $\alpha-$stable processes on the Sierpi\'nski gasket $\mathcal G,$ evolving among killing Poissonian obstacles. Simultaneously, we derive the large-time asymptotics for the volume of the $\alpha-$stable sausage on the gasket.