Log-concave perturbations of the exponential measure preserve Poincaré constants up to logarithmic growth in dimension, giving near-optimal estimates for sections of l_p balls and symmetry results on eigenspaces of associated operators.
Gauss ian mixtures: entropy and geometric inequalities
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Spectral gaps, symmetries and log-concave perturbations
Log-concave perturbations of the exponential measure preserve Poincaré constants up to logarithmic growth in dimension, giving near-optimal estimates for sections of l_p balls and symmetry results on eigenspaces of associated operators.