Ehrhard-type inequality for the isotropic Cauchy distribution on the plane

• Autorzy: Byczkowski Tomasz , Małecki Jacek , Żak Tomasz

Identyfikatory

DOI

10.37190/0208-4147.00036

• Języki publikacji: EN

Abstrakty

EN

We prove an analogue of Ehrhard's inequality for the two-dimensional isotropic Cauchy measure. In contrast to the Gaussian case, the inequality is not valid for non-convex sets. We provide the proof for rectangles which are symmetric with respect to one coordinate axis.

Słowa kluczowe

EN

Cauchy distribution; Ehrhard-type inequality

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2022
• Tom: Vol. 42, Fasc. 1
• Strony: 163--175
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Byczkowski Tomasz

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland

autor

Małecki Jacek

• Faculty of Mathematics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Żak Tomasz

• Faculty of Mathematics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

• 1. C. Borell, The Ehrhard inequality, C. R. Math. Acad. Sci. Paris 337 (2003), 663-667.
• 2. T. Byczkowski and T. Żak, Borell and Landau-Shepp inequalities for Cauchy-type measures, Probab. Math. Statist. 41 (2021), 129-152.
• 3. A. Ehrhard, Symétrisation dans l'espace de Gauss, Math. Scand. 53 (1983), 281-301.
• 4. R. J. Gardner, The Brunn-Minkowski Inequality, Bull. Amer. Math. Soc. 39 (2002), 355-405.
• 5. R. Latała and K. Oleszkiewicz, Gaussian measures of dilations of convex symmetric sets, Ann. Probab. 27 (1999), 1922-1938.
• 6. A. Prekopa, Logarithmic concave measures with application to stochastic programming, Acta Sci. Math. (Szeged) 32 (1971), 301-316.