There is a total function whose randomized query complexity grows as Ω(R(f) log 1/ε), and every function obeys a strong direct sum theorem for average query complexity.
Separations in communication complexity using cheat sheets and information complexity
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Optimal Separation and Strong Direct Sum for Randomized Query Complexity
There is a total function whose randomized query complexity grows as Ω(R(f) log 1/ε), and every function obeys a strong direct sum theorem for average query complexity.