Sharp lower bounds ||S_p(1_A)||_1 ≳ |A|* log(1/|A|*) are established for dyadic square functions S1 and S2 on indicators, using Brownian exit times and the Takagi function.
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Dictator functions maximize Φ-stability locally for balanced Boolean functions; computer methods confirm Courtade-Kumar conjecture for ρ≤0.914 and symmetrized Li-Médard for q∈[1.36,2).
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Sharp Lower Bounds for Dyadic Square Functions of indicator functions of sets
Sharp lower bounds ||S_p(1_A)||_1 ≳ |A|* log(1/|A|*) are established for dyadic square functions S1 and S2 on indicators, using Brownian exit times and the Takagi function.
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Local Optimality of Dictator Functions with Applications to Courtade--Kumar and Li--M\'edard Conjectures
Dictator functions maximize Φ-stability locally for balanced Boolean functions; computer methods confirm Courtade-Kumar conjecture for ρ≤0.914 and symmetrized Li-Médard for q∈[1.36,2).