Solution of Shannon's problem on the monotonicity of entropy

By S. Artstein, Keith Ball, Franck Barthe, Assaf Naor. 2004

202 citations recorded by the source corpus.

Subfields: Electrical and Electronic Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7ad4968d24d68fcd9e2f431dc3f8387500f938f5

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In Electrical and Electronic Engineering

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

The (B) conjecture for the Gaussian measure of dilates of symmetric convex sets and related problems (2004, background): “In fact, for the study of the function g defined in (3), one can apply the “Basic formula” of [2], which was extended to the d-dimensional case in [1] (although not in the form (13) reproduced here).”
On the entropy of sums (2008, background): “(9) It is easy to see that this generalizes the entropy power inequalities of Shannon-Stam [10], [11] and Artstein, Ball, Barthe and Naor [12].”
Information Inequalities for Joint Distributions, With Interpretations and Applications (2008, background): “Recently the first author showed (building on work in [2] and [33]) the following generalized entropy power inequality.”
On the rate of convergence in the entropic central limit theorem (2004, methodology): “Our approach relies on the following result, which we proved in [1] Theorem 3.”
Log-Concavity and Strong Log-Concavity: a review (2014, background): “…beginnings in the work of Linnik (1959), Brown (1982), and Barron (1986), but has interesting cross-connections with log-concavity in the more recent papers of Johnson and Barron (2004), Carlen and Soffer (1991), Ball, Barthe and Naor (2003), Artstein et al. (2004a), and Artstein et al. (2004b).”
Universal Estimation of Information Measures for Analog Sources (2009, background): “These types of inequalities are useful for the examination of monotonicity in central limit theorems [13, 19, 159, 244] for independent random variables.”
Reverse Brunn–Minkowski and reverse entropy power inequalities for convex measures (2011, background): “also [21], [23], [53] for a refinement when one of the random vectors is normal, and [1], [33] for other refinements), asserts that H(X + Y ) ≥ H(X) +H(Y ), (1.”
Relative entropy of cone measures and Lp centroid bodies (2009, background): “Also, classical Brunn–Minkowski theory is related to information theoretic concepts (see, for example, [3, 4, 13, 14]).”