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}
}
  • André Schlichting
  • Published 2019
  • Mathematics, Computer Science
  • Entropy
  • 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

    Topics from this paper.

    Entropy and Information Inequalities

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 21 REFERENCES
    On fine properties of mixtures with respect to concentration of measure and Sobolev type inequalities
    14
    Logarithmic Sobolev inequalities for unbounded spin systems revisited
    14
    The Eyring-Kramers formula for Poincaré and logarithmic Sobolev inequalities
    8
    Logarithmic Sobolev Inequalities for Unbounded Spin Systems Revisited
    82
    Exponential Integrability and Transportation Cost Related to Logarithmic Sobolev Inequalities
    466