Logarithmic Sobolev Inequalities

Part of the Universitext book series (UTX)


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:
$$ {J_m} \leqslant \alpha {J_{\sigma }} $$
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}.


Compact Subset Transition Function Central Limit Central Limit Theorem Sobolev Inequality 
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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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