Tree Recurrence hardcore model:i independent set I in T u( pr≌，Pr[is unoccupied by I] IouT T Wd T T Ta pz,≌，Pr[is unoccupied byI] IouTipT , Pr I⇠µT [v is unoccupied by I ] Ti v ui T hardcore model: independent set I in T µT (I) / ￾|I| Tree Recurrence pTi , Pr I⇠µTi [ui is unoccupied by I ] u1 ud T1 Td