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for questions involving inequalities, upper and lower bounds.

2 votes

Hypercontractivity of two simple random variables, $E[XY]^s \le E[X^s]E[Y^s].$

Define $q_1 = p_{11} + p_{12}$ and $q_2 = p_{11} + p_{21}$ and set $$ f(1) = \sqrt[s]{\frac{\frac{1}{2} + x}{q_1}} $$ $$ f(-1) = \sqrt[s]{\frac{\frac{1}{2} - x}{1 - q_1}} $$ $$ g(1) = \sqr …
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