Bounds on the Poincaré constant for convolution measures

  title={Bounds on the Poincar{\'e} constant for convolution measures},
  author={Thomas A. Courtade},
  • T. Courtade
  • 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
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