Logarithmic Sobolev inequalities and concentration of measure for convex functions and polynomial chaoses

• Autorzy: Adamczak R.

Identyfikatory

DOI

10.4064/ba53-2-10

• Języki publikacji: EN

Abstrakty

EN

We prove logarithmic Sobolev inequalities and concentration results for convex functions and a class of product random vectors. The results are used to derive tail and moment inequalities for chaos variables (in the spirit of Talagrand and Arcones-Gine). We also show that the same proof may be used for chaoses generated by log-concave random variables, recovering results by Łochowski, and present an application to exponential integrability of Rademacher chaos.

Słowa kluczowe

EN

log-Sobolev inequalities; concentration of measure; polynomial chaos

PL

nierówność logarytmiczna Sobolewa; koncentracja miary; chaos wielomianowy

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: Vol. 53, no 2
• Strony: 221--238
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Adamczak R.

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P. O. Box 21, 00-956 Warszawa 10, Poland,

Bibliografia

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