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Logarithmic Sobolev Inequalities

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Part of the Universitext book series (UTX)

Abstract

There is an interesting connection between our considerations here and L. Gross’s theory of logarithmic Sobolev inequalities. For our purposes, it is best to describe a logarithmic Sobolev inequality in the following terms. Let {Px: x ∈ E} satisfy (S.C.) with respect to m ∈ m1 (E). A logarithmic Sobolev inequality is a statement of the form:
$$ {J_m} \leqslant \alpha {J_{\sigma }} $$
(9.1)
for some α > 0, where Jm: m1(E) → [0, ∞) ∪ {∞} is defined by: Obviously, (9.1) has interesting implications for the large deviation theory associated with {Px: x ∈ E}.

Keywords

Compact Subset Transition Function Central Limit Central Limit Theorem Sobolev Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1984

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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