Related papers: An information-theoretic proof of a hypercontracti…

We provide a proof of the sharp log-Sobolev inequality on a compact interval.

We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.

An technically interesting proof of a known theorem.

The present paper offers, in its first part, a unified approach for the derivation of families of inequalities for set functions which satisfy sub/supermodularity properties. It applies this approach for the derivation of information…

In this paper we provide a new Bennequin-type inequality for the Rasmussen- Beliakova-Wehrli invariant, featuring the numerical transverse braid invariants (the c-invariants) introduced by the author. From the Bennequin type-inequality, and…

The hypercontractivity is proved for the Markov semigroup associated to a class of finite/infinite dimensional stochastic Hamiltonian systems. Consequently, the Markov semigroup is exponentially convergent to the invariant probability…

In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in…

In this article, we study a class of contractive factors of $m$-hypercontractions for $m \in \mathbb{N}$. We find a characterization of such factors and this is achieved by finding explicit dilation of these factors on some weighted Bergman…

A Stein-Tomas type inequality and a (weak) decoupling inequality are proved by using the polynomial partitioning method. Both estimates are related closely to Waring's problem.

We prove some extensions of Andrews inequality.

We provide a simple example showing that some conditional information inequalities (even in a weak form) cannot be derived from unconditional inequalities.

In this paper, we use certain norm inequalities to obtain new uncertain relations based on the Wigner-Yanase skew information. First for an arbitrary finite number of observables we derive an uncertainty relation outperforming previous…

Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.

We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.

In this note we prove optimal inequalities for bounded functions in terms of their deviation from their mean. These results extend and generalize some known inequalities due to Thong (2011) and Perfetti (2011)

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.

In this paper we present a complete proof of a conjecture due to V. V. Prelov in 2010 about an information inequality for the binary entropy function.

In this note we show that McGee's {\omega}-inconsistency result can be derived from L\"ob's theorem.

A generalized skew information is defined and a generalized uncertainty relation is established with the help of a trace inequality which was recently proven by J.I.Fujii. In addition, we prove the trace inequality conjectured by S.Luo and…

We prove a new extremal inequality, motivated by the vector Gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problems. As a corollary, this inequality yields a generalization of the…