More on Talagrand's inequality and the spectral method

I will continue our discussion of techniques for proving superconcentration paricularly in energy models. Specifically, we'll cover why Talagrand's inequality is useful for monotone functions but not some others, and we'll analyze the Ornstein-Uhlenbeck process in more detail to provide an alternate superconcentration proof strategy via Hermite polynomial eigenfunctions. The talk will mostly cover parts of Chapter 5 and 6 of Chatterjee's book.