About: Logarithmic Sobolev inequalities

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In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f, its logarithm, and its gradient . These inequalities were discovered and named by Leonard Gross, who established them in dimension-independent form, in the context of constructive quantum field theory. Similar results were discovered by other mathematicians before and many variations on such inequalities are known. Gross proved the inequality: In particular, a probability measure on is said to satisfy the log-Sobolev inequality with constant if for any smooth function f

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  • In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f, its logarithm, and its gradient . These inequalities were discovered and named by Leonard Gross, who established them in dimension-independent form, in the context of constructive quantum field theory. Similar results were discovered by other mathematicians before and many variations on such inequalities are known. Gross proved the inequality: where is the -norm of , with being standard Gaussian measure on Unlike classical Sobolev inequalities, Gross's log-Sobolev inequality does not have any dimension-dependent constant, which makes it applicable in the infinite-dimensional limit. In particular, a probability measure on is said to satisfy the log-Sobolev inequality with constant if for any smooth function f where is the entropy functional. (en)
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  • In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f, its logarithm, and its gradient . These inequalities were discovered and named by Leonard Gross, who established them in dimension-independent form, in the context of constructive quantum field theory. Similar results were discovered by other mathematicians before and many variations on such inequalities are known. Gross proved the inequality: In particular, a probability measure on is said to satisfy the log-Sobolev inequality with constant if for any smooth function f (en)
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  • Logarithmic Sobolev inequalities (en)
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