A Simpler Proof of the Negative Association Property for Absolute Values of Measures Tied to Generalized Orlicz Balls

• Autorzy: Jakub Onufry Wojtaszczyk
• Języki publikacji: EN

Abstrakty

EN

Negative association for a family of random variables $(X_i)$ means that for any coordinatewise increasing functions f,g we have
$𝔼 (X_{i₁},...,X_{i_k}) g(X_{j₁},...,X_{j_l}) ≤ 𝔼 f(X_{i₁},...,X_{i_k}) 𝔼 g(X_{j₁},...,X_{j_l})$
for any disjoint sets of indices (iₘ), (jₙ). It is a way to indicate the negative correlation in a family of random variables. It was first introduced in 1980s in statistics by Alem & Saxena and Joag-Dev & Proschan, and brought to convex geometry in 2005 by Wojtaszczyk & Pilipczuk to prove the Central Limit Theorem for Orlicz balls. The paper gives a relatively simple proof of negative association of absolute values for a wide class of measures tied to generalized Orlicz balls, including the uniform measures on such balls.

Kategorie tematyczne

• 60D05: Geometric probability and stochastic geometry
• 52A20: Convex sets in n dimensions (including convex hypersurfaces)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: 57
• Numer: 1
• Strony: 41-56

Daty

wydano

2009

Twórcy

autor

Jakub Onufry Wojtaszczyk

• Department of Mathematics, Computer Science and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba57-1-5