紧群的极大熵
Maximum Entropy on Compact Groups
摘要：
在紧群上，Haar概率测度起着均匀分布的作用。研究了这种均匀分布下的熵和率失真理论。给出了紧群上卷积收敛性的新结果和简化证明，它们可以表述为熵增加到最大。信息理论技术和马尔可夫链起着至关重要的作用。收敛结果也制定通过率失真函数。收敛速度是指数的。
英文摘要：
On a compact group the Haar probability measure plays the role of uniform distribution. The entropy and rate distortion theory for this uniform distribution is studied. New results and simplified proofs on convergence of convolutions on compact groups are presented and they can be formulated as entropy increases to its maximum. Information theoretic techniques and Markov chains play a crucial role. The convergence results are also formulated via rate distortion functions. The rate of convergence is shown to be exponential.
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