|Location:||MSRI: Simons Auditorium|
The log-Sobolev inequality (LSI) is a very useful tool for analyzinghigh-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.