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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… Expand

Upper bounds for symmetric Markov transition functions

- E. Carlen, S. Kusuoka, D. Stroock
- Mathematics
- 1 June 1986

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… Expand

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… Expand

Superadditivity of Fisher's information and logarithmic Sobolev inequalities

- E. Carlen
- Mathematics
- 1 October 1991

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… Expand

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… Expand

Entropy and chaos in the Kac model

- E. Carlen, M. C. Carvalho, J. Roux, M. Loss, C. Villani
- Mathematics, Physics
- 23 August 2008

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… Expand

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… Expand

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… Expand

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… Expand

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