Chapter 10 notes

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Chapter 10 exercises

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Chapter 10: Advanced hypercontractivity

In this chapter we complete the proof of the Hypercontractivity Theorem for uniform $\pm 1$ bits. We then generalize the $(p,2)$ and $(2,q)$ statements to the setting of arbitrary product probability spaces, proving the following:

The General Hypercontractivity Theorem Let $(\Omega_1, \pi_1), \dots, (\Omega_n, \pi_n)$ be finite probability spaces, in each of which [...]