Analyticity of the entropy and the escape rate of random walks in hyperbolic groups
Analyticity of the entropy and the escape rate of random walks in hyperbolic groups
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双曲群中随机游走的熵和逃逸率的解析性
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发表时间：
2015
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通讯作者：
S. Gouezel
中科院分区：
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作者：
S. Gouezel
我们考虑了具有字距离的非初等双曲群上的随机游动。对于群上的概率测度，有两个数值量，即逃逸率和熵。在一组允许的概率测度，其支持包含在一个给定的有限集，我们表明，这两个数量依赖于概率测度的分析方法。我们的谱技术也给出了一个新的证明的中心极限定理，并意味着相应的方差是解析的。
We consider random walks on a non-elementary hyperbolic group endowed with a word distance. To a probability measure on the group are associated two numerical quantities, the rate of escape and the entropy. On the set of admissible probability measures whose support is contained in a given finite set, we show that both quantities depend in an analytic way on the probability measure. Our spectral techniques also give a new proof of the central limit theorem, and imply that the corresponding variance is analytic.