论文标题
广义熵力的凹陷
The concavity of generalized entropy powers
论文作者
论文摘要
在本说明中，我们介绍了一个与广义熵有关的新系列熵功能，称为Sharma-Mittal熵，我们证明了它们沿相应熵功能的$ l^2 $ wasserstein梯度流产生的扩散过程。该结果扩展了Savaré和Toscani对Rényi熵力量的凹度的结果（IEEETrans。Inf。Theolode，2014年），并揭示了Bobkov和Marsiglietti（IEEE EEEETrans。Inf。Inf。Theolode，2017年）与Rényi熵功率不平等的联系。
In this note we introduce a new family of entropy powers which are related to generalized entropies, called Sharma-Mittal entropies, and we prove their concavity along diffusion processes generated by $L^2$-Wasserstein gradient flows of corresponding entropy functionals. This result extends the result of Savaré and Toscani on the concavity of Rényi entropy powers (IEEE Trans. Inf. Theory, 2014) and reveals a connection to Rényi entropy power inequalities by Bobkov and Marsiglietti (IEEE Trans. Inf. Theory, 2017).
