Theorem (Feng,Sun,Y.'17): For any△≥6，any distributed algorithm that samples uniform independent set within bounded total variation distance in graphs with max-degree A requires (diam)rounds of communications. A strong separation of sampling from other local computation tasks: Independent set is trivial to construct locally(because is an independent set). The (diam)lower bound for sampling holds even when every vertex knows the entire graph: The lower bound holds not because of the locality of input information,but because of the locality of randomness.Theorem (Feng, Sun, Y. ’17): For any ∆≥6, any distributed algorithm that samples uniform independent set within bounded total variation distance in graphs with max-degree ∆ requires Ω(diam) rounds of communications. • Independent set is trivial to construct locally (because ∅ is an independent set). • The Ω(diam) lower bound for sampling holds even when every vertex knows the entire graph: • The lower bound holds not because of the locality of input information, but because of the locality of randomness. A strong separation of sampling from other local computation tasks: