Chapter 10 notes


Chapter 10 exercises


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 [...]