Skip to content

An extremal property of the normal distribution, with a discrete analog

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)181-186
Number of pages6
JournalStatistics and Probability Letters
Volume145
Early online date25 Sep 2018
DOIs
DateAccepted/In press - 26 Aug 2018
DateE-pub ahead of print - 25 Sep 2018
DatePublished (current) - Feb 2019

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.

    Research areas

  • Brascamp–Lieb inequality, Characterization of laws, Chebychev's other inequality, Log-concavity, Normal distribution, Poisson distribution

Download statistics

No data available

Documents

Documents

  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Elsevier at https://www.sciencedirect.com/science/article/pii/S0167715218302931?via%3Dihub. Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 140 KB, PDF document

    Licence: CC BY-NC-ND

Links

DOI

View research connections

Related faculties, schools or groups