An inequality between total variation and L2 distances for polynomials in log-concave random vectors

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Abstract

In the paper we discuss a new bound of the total variation distance in terms of L2 distance for random variables that are polynominals in log-concave random vectors.

About the authors

E. D. Kosov

Lomonosov Moscow State University; Higher School of Economics

Author for correspondence.
Email: ked_2006@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991; 20, Myasnitskaya str., Moscow, 101000

References

  1. Давыдов Ю.А., Мартынова Г.В. В сб.: Статистика и управление случайными процессами. М.: Наука, 1987. С. 55-57.
  2. Мартынова Г.В. // Диссертация канд. физ.-мат. наук. 01.01.05. Л.: ЛГУ, 1987; № 1-1-5/ЛГУ. Рос. гос. библиотека (М.).
  3. Nourdin I., Poly G. // Stochastic Processes Appl. 2013. V. 123. № 2. P. 651-674.
  4. Bogachev V.I., Kosov E.D., Zelenov G.I. // Trans. Amer. Math. Soc. 2018. V. 370. № 6. P. 4401-4432.
  5. Zelenov G.I. // Theory Stoch. Processes. 2017. V. 38. № 2. P. 79-85.
  6. Kosov E.D. // J. Math. Anal. Appl. 2018. V. 462. № 1. P. 390-406.
  7. Кругова Е.П. // Мат. сб. 1997. Т. 188. № 2. С. 57-66.
  8. Klartag B. // Geom. & Funct. Anal. GAFA. 2006. V. 16. № 6. P. 1274-1290.
  9. Klartag B.// J. Funct. Anal. 2007. V. 245. № 1. P. 284-310.
  10. Klartag B. // Inventiones Math. 2007. V. 168. № 1. P. 91-131.
  11. Bobkov S.G. // Geom. & Funct. Anal. GAFA. 2000. V. 1745. P. 27-35.
  12. Bobkov S.G. // Теор. вероятн. и примен. 2000. V. 45. № 4. С. 745-748.
  13. Carbery A., Wright J. // Math. Res. Lett. 2001. V. 8. № 3. P. 233-248.
  14. Bobkov S.G. // Ann. Probab. 1999. V. 27. № 4. P. 1903-1921.
  15. Fradelizi M., Guédon O. // Discrete Comput. Geom. 2004. V. 31. № 2. P. 327-335.

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