Yao Gan

Sharp quantum logarithmic Sobolev inequalities via semigroup interpolation

We develop a semigroup interpolation method for sharp logarithmic Sobolev inequalities using spectral calculus and estimates of $\mathrm{Re}\langle\,Lx,x^2\rangle_2$, where $L$ generates an auxiliary symmetric quantum Markov semigroup. We apply the method to free groups and to crossed products of a finite von Neumann a...