Theory of Probability and Mathematical Statistics
The Poincaré inequality and logarithmic Sobolev inequality for a spherically censored Gaussian measure
T. D. Tymoshkevych
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Abstract: For a one-dimensional projection of a spherically censored Gaussian measure on R^n, the logarithmic Sobolev inequality is proved. As a consequence, we obtain the Poincaré inequality for a spherically censored Gaussian measure on R^n, n≥3.
Keywords: Logarithmic Sobolev inequality, Poincaré inequality, censored Gaussian measure
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