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The Poincaré inequality and logarithmic Sobolev inequality for a spherically censored Gaussian measure


Author: T. D. Tymoshkevych
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 91 (2014).
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
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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 $.


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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

DOI: https://doi.org/10.1090/tpms/976
Keywords: Logarithmic Sobolev inequality, Poincar\'e inequality, censored Gaussian measure
Received by editor(s): September 4, 2014
Published electronically: February 4, 2016
Article copyright: © Copyright 2016 American Mathematical Society