# Bounds on the Poincaré constant for convolution measures

@article{Courtade2018BoundsOT,
title={Bounds on the Poincar{\'e} constant for convolution measures},
journal={ArXiv},
year={2018},
volume={abs/1807.00027}
}
• Published 29 June 2018
• Computer Science, Mathematics
• ArXiv
We establish a Shearer-type inequality for the Poincar\'e constant, showing that the Poincar\'e constant corresponding to the convolution of a collection of measures can be nontrivially controlled by the Poincar\'e constants corresponding to convolutions of subsets of measures. This implies, for example, that the Poincar\'e constant is non-increasing along the central limit theorem. We also establish a dimension-free stability estimate for subadditivity of the Poincar\'e constant on… Expand
13 Citations

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