Jonathan Ben-Artzi - Mind the gap: what to do if the generator of your Markov semigroup is missing its spectral gap

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In this general audience talk, we will combine tools from analysis (and in particular spectral analysis) and probability theory to investigate time decay properties of various physical systems (such as the spreading of heat inside some volume). It is well-known that a spectral gap is equivalent to a so called Poincaré inequality and to an exponential rate of decay. After explaining these notions, we will see how some of these results can be extended to cases where there is no spectral gap. This is joint work with Amit Einav (Graz).