Analysis and geometry of Markov diffusion operators

By David Applebaum. Mathematical Gazette, 2016

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Data-driven approximation of the Koopman generator: Model reduction, system identification, and control (2019, unknown): “The generator L is self-adjoint on L(2)μ(X) and it can be shown that, assuming suitable growth conditions on the potential, the spectrum of L is discrete [33].”
Bourgain’s slicing problem and KLS isoperimetry up to polylog (2022, background): “We refer the reader to [2, 18, 20] for standard background on spectral theory.”
Theoretical guarantees for approximate sampling from smooth and log‐concave densities (2014, unknown): “Therefore, according to Chen and Wang (1997), remark 4.14, and Bakry et al. (2014), corollary 4.8.2, the process Lt is geometrically ergodic in L2.”