Entropy and Convergence on Compact Groups
Entropy and Convergence on Compact Groups
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紧群上的熵和收敛性
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
Y. Suhov
中科院分区：
文献类型：
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作者：
O. Johnson;Y. Suhov
我们研究紧群上独立随机变量的卷积熵的行为。我们提供了熵收敛到最大值的速率的显式指数界限。同样，这证明了库尔贝克-莱布勒意义上的密度收敛于均匀性。我们证明这种收敛严格地存在于密度一致收敛（如 Shlosman 和 Major 所研究的）和弱收敛（经典 Ito-Kawada 定理的含义）之间。事实上它介于 L1+ε 的收敛性和 L1 的收敛性之间。
We investigate the behaviour of the entropy of convolutions of independent random variables on compact groups. We provide an explicit exponential bound on the rate of convergence of entropy to its maximum. Equivalently, this proves convergence of the density to uniformity, in the sense of Kullback–Leibler. We prove that this convergence lies strictly between uniform convergence of densities (as investigated by Shlosman and Major), and weak convergence (the sense of the classical Ito–Kawada theorem). In fact it lies between convergence in L1+ε and convergence in L1.