62 citations · 79 across the 5 of their papers we have counts for
5 papers
Logarithmic Sobolev inequalities in discrete product spaces: a proof by a transportation cost distance
Katalin Marton
The aim of this paper is to prove an inequality between relative entropy and the sum of average conditional relative entropies of the following form: For a fixed probability measur…
An inequality for relative entropy and logarithmic Sobolev inequalities in Euclidean spaces
Katalin Marton
Let and denote density functions on the -dimensional Euclidean space, and let and $Q_i(\cdot|x_1,..., x_{i-1},x_{i+1…
Bounding relative entropy by the relative entropy of local specifications in product spaces
Katalin Marton
For a class of density functions on we prove an inequality between relative entropy and the sum of average conditional relative entropies of the following for…
An explicit bound on the Logarithmic Sobolev constant of weakly dependent random variables
Katalin Marton
We prove logarithmic Sobolev inequality for measures under the assumptions that: (i) the conditional…
Measure concentration for Euclidean distance in the case of dependent random variables
Katalin Marton
Let q^n be a continuous density function in n-dimensional Euclidean space. We think of q^n as the density function of some random sequence X^n with values in \BbbR^n. For I\subset[…