The log-Sobolev inequality (LSI) is a very useful tool for analyzing
high-dimensional situations. For example, the LSI can be used for
deriving hydrodynamic limits, for estimating the error in stochastic
homogenization, for deducing upper bounds on the mixing times of Markov
chains, and even in the proof of the Poincaré conjecture by
Perelman. For most applications, it is crucial that the constant in the
LSI is uniform in the size of the underlying system. In this talk, we
discuss when to expect a uniform LSI in the setting of unbounded spin
systems. We will also explain a connection to the KLS conjecture.