Small ball probability estimates in terms of width

• Autorzy: Rafał Latała , Krzysztof Oleszkiewicz
• Języki publikacji: EN

Abstrakty

EN

A certain inequality conjectured by Vershynin is studied. It is proved that for any symmetric convex body K ⊆ ℝⁿ with inradius w and γₙ(K) ≤ 1/2 we have $γₙ(sK) ≤ (2s)^{w²/4}γₙ(K)$ for any s ∈ [0,1], where γₙ is the standard Gaussian probability measure. Some natural corollaries are deduced. Another conjecture of Vershynin is proved to be false.

Kategorie tematyczne

• 60G15: Gaussian processes
• 60E15: Inequalities; stochastic orderings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 169
• Numer: 3
• Strony: 305-314

Daty

wydano

2005

Twórcy

autor

Rafał Latała

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

autor

Krzysztof Oleszkiewicz

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland

Identyfikatory

DOI

10.4064/sm169-3-6