Abstract
We give a new proof, using only the Brascamp–Lieb inequality, of the fact that the Gaussian measure is the only strong log-concave measure having a strong log-concavity parameter equal to its covariance matrix. We unify the continuous and discrete settings by also giving a similar characterization of the Poisson measure in the discrete case, using “Chebyshev’s other inequality”. We briefly discuss how these results relate to Stein and Stein–Chen methods for Gaussian and Poisson approximation, and to the Bakry–Émery calculus.
Original language | English |
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Pages (from-to) | 181-186 |
Number of pages | 6 |
Journal | Statistics and Probability Letters |
Volume | 145 |
Early online date | 25 Sept 2018 |
DOIs | |
Publication status | Published - Feb 2019 |
Keywords
- Brascamp–Lieb inequality
- Characterization of laws
- Chebychev's other inequality
- Log-concavity
- Normal distribution
- Poisson distribution