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Explore a lecture on Boolean functions and their behavior under random restrictions. Delve into the probability of Boolean functions with small max influence becoming constant, focusing on functions with variance of Ω(1) and individual influences bounded by τ. Discover how restricting all but a fraction of coordinates affects the function's constancy. Examine the optimal bound demonstrated by the tribes function. Investigate an extension to anti-concentration results, revealing insights into the variance of restricted functions. Learn about the sharp version of the "it ain't over till it's over" theorem by Mossel, O'Donnell, and Oleszkiewicz. Gain valuable knowledge from this joint work by Pei Wu, Avi Wigderson, and Ronen Eldan, presented at the Simons Institute.
