Related papers: An information-theoretic proof of a hypercontracti…
We improve constants in the Rademacher-Menchov inequality.
Two new proofs of the Fisher information inequality (FII) using data processing inequalities for mutual information and conditional variance are presented.
In this paper we provide a new inequality useful for the proofs of strong converse theorems in the multiterminal information theory. We apply this inequality to the recent work by Tyagi and Watanabe on the strong converse theorem for the…
We show that the inequality $H(A \mid B,X) + H(A \mid B,Y) \le H(A\mid B)$ for jointly distributed random variables $A,B,X,Y$, which does not hold in general case, holds under some natural condition on the support of the probability…
A short, information-theoretic proof of the Kac--Bernstein theorem, which is stated as follows, is presented: For any independent random variables $X$ and $Y$, if $X+Y$ and $X-Y$ are independent, then $X$ and $Y$ are normally distributed.
Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous spaces. In this survey we trace a few connections between different manifestations of…
In this note we prove an inequality involving primes and the product of consecutive primes.
We present a simple proof of the entropy-power inequality using an optimal transportation argument which takes the form of a simple change of variables. The same argument yields a reverse inequality involving a conditional differential…
We provide necessary and sufficient conditions for hypercontractivity of the minima of nonnegative, i.i.d. random variables and of both the maxima of minima and the minima of maxima for such r.v.'s. It turns out that the idea of…
We generalize a result by Carlen and Cordero-Erausquin on the equivalence between the Brascamp-Lieb inequality and the subadditivity of relative entropy by allowing for random transformations (a broadcast channel). This leads to a unified…
A family of skew information quantities is obtained, in which the well-known Wigner-Yanase skew information and quantum Fisher information stand as special cases. A transparent proof of convexity of the generalized skew information is…
This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.
We establish analogues of the Bergstr\"om and Bonnesen inequalities, related to determinants and volumes respectively, for the entropy power and for the Fisher information. The obtained inequalities strengthen the well-known convolution…
We establish a reversal of Lyapunov's inequality for monotone log-concave sequences, settling a conjecture of Havrilla-Tkocz and Melbourne-Tkocz. A strengthened version of the same conjecture is disproved through counter example. We also…
The article provides a counterexample to a conjecture by Blocki-Zwonek.
Recently, in paper published in the Annals of Mathematics, it was shown that the Bohnenblust-Hille inequality for (complex) homogeneous polynomials is hypercontractive. However, and to the best of our knowledge, there is no result providing…
This paper gives an overview about particular quasi-entropies, generalized quantum covariances, quantum Fisher informations, skew-informations and their relations. The point is the dependence on operator monotone functions. It is proven…
We prove a counterpart of the log-convex density conjecture in the hyperbolic plane.
We prove the self-improvement of a pointwise $p$-Hardy inequality. The proof relies on maximal function techniques and a characterization of the inequality by curves.
We prove a reverse form of the multidimensional Brascamp-Lieb inequality. Our method also gives a new way to derive the Brascamp-Lieb inequality and is rather convenient for the study of equality cases.