The Poincaré inequality and logarithmic Sobolev inequality for a spherically censored Gaussian measure
Author:
T. D. Tymoshkevych
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 91 (2015), 181-191
MSC (2010):
Primary 26D10, 39B62, 47D07, 60E15, 60J60
DOI:
https://doi.org/10.1090/tpms/976
Published electronically:
February 4, 2016
MathSciNet review:
3364133
Full-text PDF Free Access
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Abstract: For a one-dimensional projection of a spherically censored Gaussian measure on $\mathbf {R}^{n}$, the logarithmic Sobolev inequality is proved. As a consequence, we obtain the Poincaré inequality for a spherically censored Gaussian measure on $\mathbf {R}^{n}$, $n \geq 3$.
References
- Alexei M. Kulik and Taras D. Tymoshkevych, Lift zonoid order and functional inequalities, Teor. Ĭmovīr. Mat. Stat. 89 (2013), 75–90 (English, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 89 (2014), 83–99. MR 3235177, DOI https://doi.org/10.1090/s0094-9000-2015-00937-6
- E. Boissard, P. Cattiaux, A. Guillin, and L. Miclo, Ornstein–Uhlenbeck pinball: I. Poincaré inequalities in a punctured domain, arXiv:1309.0986v1.
- Dominique Bakry and Michel Émery, Hypercontractivité de semi-groupes de diffusion, C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), no. 15, 775–778 (French, with English summary). MR 772092
- Michel Ledoux, Concentration of measure and logarithmic Sobolev inequalities, Séminaire de Probabilités, XXXIII, Lecture Notes in Math., vol. 1709, Springer, Berlin, 1999, pp. 120–216. MR 1767995, DOI https://doi.org/10.1007/BFb0096511
References
- A. Kulik and T. Tymoshkevych, Lift zonoid order and functional inequalities, Teor. Imovirnost. Matem. Statyst. 89 (2013), 75–90; English transl. in Theor. Probability and Math. Statist. 89 (2014), 83–99. MR 3235177
- E. Boissard, P. Cattiaux, A. Guillin, and L. Miclo, Ornstein–Uhlenbeck pinball: I. Poincaré inequalities in a punctured domain, arXiv:1309.0986v1.
- D. Bakry and M. Émery, Hypercontractivité de semi-groupes de diffusion, C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), no. 15, 775–778. MR 772092 (86f:60097)
- M. Ledoux, Concentration of measure and logarithmic Sobolev inequalities, Séminaire de probabilités (Strasbourg) XXXIII (1999), 120–216; Lecture Notes in Math., vol. 1709, Springer, Berlin. MR 1767995 (2002j:60002)
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Additional Information
T. D. Tymoshkevych
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email:
tymoshkevych@gmail.com
Keywords:
Logarithmic Sobolev inequality,
Poincaré inequality,
censored Gaussian measure
Received by editor(s):
September 4, 2014
Published electronically:
February 4, 2016
Article copyright:
© Copyright 2016
American Mathematical Society
