# Poincaré and Log-Sobolev Inequalities for Mixtures

@article{Schlichting2019PoincarAL, title={Poincar{\'e} and Log-Sobolev Inequalities for Mixtures}, author={Andr{\'e} Schlichting}, journal={Entropy}, year={2019}, volume={21}, pages={89} }

This work studies mixtures of probability measures on R n and gives bounds on the Poincare and the log–Sobolev constants of two-component mixtures provided that each component satisfies the functional inequality, and both components are close in the χ 2 -distance. The estimation of those constants for a mixture can be far more subtle than it is for its parts. Even mixing Gaussian measures may produce a measure with a Hamiltonian potential possessing multiple wells leading to metastability and… CONTINUE READING

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