A short proof of the "Concavity of entropy power"

نویسنده

  • Cédric Villani
چکیده

We give a simple proof of the “concavity of entropy power”.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An information-theoretic proof of Nash's inequality

We show that an information-theoretic property of Shannon's entropy power, known as concavity of entropy power [7], can be fruitfully employed to prove inequalities in sharp form. In particular, the concavity of entropy power implies the logarithmic Sobolev inequality, and the Nash's inequality with the sharp constant.

متن کامل

On the analogue of the concavity of entropy power in the Brunn-Minkowski theory

Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured in On the similarity of the entropy power inequality and the BrunnMinkowski inequality (IEEE Trans. Inform. Theory 30 (1984), no. 6, 837-839) the 1 n -concavity of the outer parallel volume of measurable sets as an analogue of the concavity of entropy power. We inve...

متن کامل

Tsallis Entropy and Conditional Tsallis Entropy of Fuzzy Partitions

The purpose of this study is to define the concepts of Tsallis entropy and conditional Tsallis entropy of fuzzy partitions and to obtain some results concerning this kind entropy. We show that the Tsallis entropy of fuzzy partitions has the subadditivity and concavity properties. We study this information measure under the refinement and zero mode subset relations. We check the chain rules for ...

متن کامل

A SHORT PROOF FOR THE EXISTENCE OF HAAR MEASURE ON COMMUTATIVE HYPERGROUPS

In this short note, we have given a short proof for the existence of the Haar measure on commutative locally compact hypergroups based on functional analysis methods by using Markov-Kakutani fixed point theorem.

متن کامل

The concavity of Rènyi entropy power

We associate to the p-th Rényi entropy a definition of entropy power, which is the natural extension of Shannon’s entropy power and exhibits a nice behaviour along solutions to the p-nonlinear heat equation in Rn. We show that the Rényi entropy power of general probability densities solving such equations is always a concave function of time, whereas it has a linear behaviour in correspondence ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • IEEE Trans. Information Theory

دوره 46  شماره 

صفحات  -

تاریخ انتشار 2000