Spectral Gap and Concentration for Some Spherically Symmetric Probability Measures

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Functional Inequalities for Heavy Tailed Distributions and Application to Isoperimetry (2010, background): “This recover (with 14 instead of 13) one particular result of Bobkov [18].”
Spectral gap for spherically symmetric log-concave probability measures, and beyond (2014, background): “Recently, Bobkov [4] obtained a nice estimate on the spectral gap for a class of log-concave probability measures.”
Semi Log-Concave Markov Diffusions (2013, unknown): “For the Poincaré constant, it was shown by Bobkov [8] that 1 n Varµ(x) ≤ CP (µ) ≤ 13 n Varµ(x) .”
Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes (2016, background): “[4]), whereas our lower bound for the contraction rate is of order Ω(d−2 log−2(d)).”
Concentration of the information in data with log-concave distributions (2010, methodology): “This is proved in [5] by an application of the Pr´ekopa–Leindler inequality, and is perhaps more convenient for applications involving asymptotics.”
Log-Concavity and Strong Log-Concavity: a review (2014, background): “It is worth noticing that when X is a log-concave vector in Rd with spherically invariant distribution, then the Euclidian norm of X , denoted ‖X‖, follows a log-concave distribution of order d − 1 (this is easily seen by transforming to polar coordinates; see Bobkov (2003) for instance).”