In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f, its logarithm, and its gradient ∇ f ...

f 2 log f 2dx ≤ log. (. Cm. ∫. R m. |∇f |2dx. ) ,. ∫. R m f 2dx = 1 form of logarithmic Sobolev inequality formally come back to Sobolev (worse constants).

Logarithmic Sobolev inequalities under the invariant measure only concern finite (normalized) measures μ. It should be mentioned that logarithmic Sobolev ...

Higher order logarithmic Sobolev inequalities have been studied by G. Feissner [2, 3]. Among his results we mention, by way of example, that if the second ...

This course is a modern overview on logarithmic Sobolev inequalities, from the probabilistic side. These inequalities have been the subject of intense ...

We introduce log-Sobolev inequalities for analyzing mixing time of random walks, and see that they provide the optimal bound for the down-up walks on strongly ...

Jan 13, 2021 · Abstract:Logarithmic Sobolev inequalities are a fundamental class of inequalities that play an important role in information theory.

Abstract. A logarithmic Sobolev inequality, analogous to Gross' inequality, is proved on the circle. From this inequality it follows that the Poisson and heat ...

Logarithmic Sobolev inequalities are a well-studied technique for estimating rates of conver- gence of Markov chains to their stationary distributions. In ...

Abstract. This is an expository paper on the use of logarithmic Sobolev inequalities for bounding rates of convergence of Markov chains on finite state spaces ...