Entropy production by block variable summation and central limit theorems
Entropy production by block variable summation and central limit theorems
复制标题
通过块变量求和和中心极限定理产生熵
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
A. Soffer
中科院分区：
文献类型：
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作者：
E. Carlen;A. Soffer
我们证明了一个严格的下限时，独立的随机变量的总和和重新标度的熵产生。利用这一点，我们开发了一种方法，从动力学的角度来看，其中的熵是一个李雅普诺夫函数的高斯极限管理方法的中心极限定理。这种动力学方法自然地扩展到涵盖因变量，并导致纯概率论以及统计力学的新结果。它还提供了一个统一的框架内，许多以前的结果很容易得出。
We prove a strict lower bound on the entropy produced when independent random variables are summed and rescaled. Using this, we develop an approach to central limit theorems from a dynamical point of view in which the entropy is a Lyapunov functional governing approach to the Gaussian limit. This dynamical approach naturally extends to cover dependent variables, and leads to new results in pure probability theory as well as in statistical mechanics. It also provides a unified framework within which many previous results are easily derived.