Skip to Main Content
Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

 
 

 

Lift zonoid order and functional inequalities


Authors: Alexei M. Kulik and Taras D. Tymoshkevych
Journal: Theor. Probability and Math. Statist. 89 (2014), 83-99
MSC (2010): Primary 26D10, 39B62, 47D07, 60E15, 60J60
DOI: https://doi.org/10.1090/S0094-9000-2015-00937-6
Published electronically: January 26, 2015
MathSciNet review: 3235177
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce the notion of a weighted lift zonoid, and we show that the ordering condition imposed on a measure $\mu$ and formulated in terms of the weighted lift zonoids of this measure leads to certain functional inequalities for $\mu$ such as non-linear extensions of Bobkov’s shift inequality and weighted inverse log-Sobolev inequality. The choice of the weight $K$ involved in our version of the inverse log-Sobolev inequality differs substantially from those known in the literature, and it requires that the weight $v$ involved in the definition of the weighted lift zonoid equals the divergence of the weight $K$ with respect to the initial measure $\mu$. We show that such a choice may be useful for proving the direct log-Sobolev inequality as well.


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2010): 26D10, 39B62, 47D07, 60E15, 60J60

Retrieve articles in all journals with MSC (2010): 26D10, 39B62, 47D07, 60E15, 60J60


Additional Information

Alexei M. Kulik
Affiliation: Institute of Mathematics, National Academy of Science of Ukraine, Tereshchenkivska Street 3, 01601, Kyiv, Ukraine
Email: kulik.alex.m@gmail.com

Taras D. Tymoshkevych
Affiliation: National Taras Shevchenko University of Kyiv, Academician Glushkov Avenue 4-e, 03127, Kyiv, Ukraine
Email: tymoshkevych@gmail.com

Keywords: Lift zonoid, weight, shift inequality, log-Sobolev inequality
Received by editor(s): September 4, 2013
Published electronically: January 26, 2015
Additional Notes: The second author was partially supported by the Leonard Euler program, DAAD project # 55518603
Article copyright: © Copyright 2015 American Mathematical Society