题目：Completely monotone conjecture for the Rényi entropy
报告人：吴浩 (南开大学统计与数据科学学院博士生)
时间：2024年6月5日（星期三）10:30-11:30
地点：正心楼616
摘要：The completely monotone conjecture states that the signs of the derivatives of the Shannon entropy along the heat flow with respect to time change alternately as the order of the derivatives increases. We investigate the completely monotone conjecture for the Rényi entropy. We confirm this conjecture for the order of derivative up to 3, when the parameter of Rényi entropy is in certain regimes. We also investigate concavity of Rényi entropy power and the complete monotonicity of Tsallis entropy. We observe that the complete monotonicity holds for Tsallis entropy of order 2, which is equivalent to say that the noise stability with respect to the heat semigroup is completely monotone. Based on this observation, we conjecture that the complete monotonicity holds for Tsallis entropy of all parameters in (1,2). Our proofs are based on the techniques of integration-by-parts, sum-of-squares, and curve-fitting.
更多信息：研究生研讨班
