互信息沿热流的凸性
Convexity of mutual information along the heat flow
摘要：
我们研究了热方程演化过程中互信息的凸性。我们证明了，如果初始分布是对数凹的，那么互信息总是时间的凸函数。我们还证明了，如果初始分布是有界的，或者具有有限的四阶矩和Fisher信息，则互信息最终是凸的，即，在所有大的时间里都是凸的。最后，我们给出了反例来说明互信息在小时间内可以是非凸的。
英文摘要：
We study the convexity of mutual information along the evolution of the heat equation. We prove that if the initial distribution is log-concave, then mutual information is always a convex function of time. We also prove that if the initial distribution is either bounded, or has finite fourth moment and Fisher information, then mutual information is eventually convex, i.e., convex for all large time. Finally, we provide counterexamples to show that mutual information can be nonconvex at small time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
