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Sharp uniform convexity and smoothness inequalities for trace norms
We prove several sharp inequalities specifying the uniform convexity and uniform smoothness properties of the Schatten trace ideals C p, which are the analogs of the Lebesgue spaces L p in
Upper bounds for symmetric Markov transition functions
Abstract : A large number of properties which are peculiar to symmetric Markov semigroups stem from the fact that such semigroups can be analyzed simultaneously by Hilbert space techniques as well as
Sharp uniform convexity and smoothness inequalities for trace norms
SummaryWe prove several sharp inequalities specifying the uniform convexity and uniform smoothness properties of the Schatten trace idealsCp, which are the analogs of the Lebesgue spacesLp in
Superadditivity of Fisher's information and logarithmic Sobolev inequalities
Abstract We prove a theorem characterizing Gaussian functions and we prove a strict superaddivity property of the Fisher information. We use these results to determine the cases of equality in the
Competing symmetries, the logarithmic HLS inequality and Onofri's inequality onsn
The sharp version of the logarithmic Hardy-Littlewood-Sobolev inequality including the cases of equality is established. We then show that this implies Beckner's generalization of Onofri's inequality
Entropy and chaos in the Kac model
We investigate the behavior in $N$ of the $N$--particle entropy functional for Kac's stochastic model of Boltzmann dynamics, and its relation to the entropy function for solutions of Kac's one
Entropy production by block variable summation and central limit theorems
We prove a strict lower bound on the entropy produced when independent random variables are summed and rescaled. Using this, we develop an approach to central limit theorems from a dynamical point of
A sharp analog of Young’s inequality on SN and related entropy inequalities
We prove a sharp analog of Young’s inequality on SN, and deduce from it certain sharp entropy inequalities. The proof turns on constructing a nonlinear heat flow that drives trial functions to
On the cases of equality in Bobkov's inequality and Gaussian rearrangement
Abstract. We determine all of the cases of equality in a recent inequality of Bobkov that implies the isoperimetric inequality on Gauss space. As an application we determine all of the cases of
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