An information-theoretic proof of Nash's inequality
نویسنده
چکیده
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.
منابع مشابه
Extracting analytic proofs from numerically solved Shannon-type Inequalities
A class of information inequalities, called Shannon-type inequalities (STIs), can be proven via a computer software called ITIP [1]. In previous work [2], we have shown how this technique can be utilized to Fourier-Motzkin elimination algorithm for Information Theoretic Inequalities. Here, we provide an algorithm for extracting analytic proofs of information inequalities. Shannon-type inequalit...
متن کاملInformation Theoretic Approach to Geometric Programming
This paper shows how the fundamental geometric inequality lemma of geometric programming can be obtained immediately from information theoretic methods. This results in a drastic simplification of the proof and points the way to other connections between information theory and geometric programming
متن کاملThe Study Feminist Tendencies and its Relationship with Economical, Social and Cultural Motives in the Female Students of the Islamic Azad University(Garmsar Branch)
The object of this research was to study and explain feminist tendencies and its relationship with economical, social, and cultural motives in the female students of the Islamic Azad University of Garmsar. It was used compilation of theoretic viewpoints of Ritzer, Castells, Giddens, and Parsons in feminist discussion and a framework and theoretic model was formulated. By using surveyor method...
متن کاملAn inequality for the binary skew-symmetric broadcast channel and its implications
We establish an information theoretic inequality concerning the binary skew-symmetric channel that was conjectured in [1]. This completes the proof that there is a gap between the inner bound[2] and the outer bound[3] for the 2receiver broadcast channel; and constitutes the first example of a provable gap between the bounds. The interesting aspect of the proof is the technique employed, and is ...
متن کاملA simple proof of the Ahlswede - Csiszár one-bit theorem
1983 931 from the second, let K = AA'. Then AA' is nonnegative definite and IAl*=+4'I < jy&L4'),i = n(l&z:.). (1) i j The implication of the second inequality from the first follows from the fact that every nonnegative definite matrix K can be factored as K = AA'. A typical proof of Hadamard's inequality is by induction (see, for example, Bellman [l]) and involves a determinant decomposition fo...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1206.2130 شماره
صفحات -
تاریخ انتشار 2012