论文标题
部分可观测时空混沌系统的无模型预测
A local limit theorem for convergent random walks on relatively hyperbolic groups
论文作者
论文摘要
We study random walks on relatively hyperbolic groups whose law is convergent, in the sense that the derivative of its Green function is finite at the spectral radius.When parabolic subgroups are virtually abelian, we prove that for such a random walk satisfies a local limit theorem of the form $p_n(e, e)\sim CR^{-n}n^{-d/2}$, where $p_n(e, e）$是返回时间$ n $，$ r $的概率，是随机步行的频谱半径的倒数，$ d $是抛物线亚组的最小等级，随机步行在光谱上是频谱退化的。这是$ p_n（e，e）$ to the comptry cance the compriencation。
We study random walks on relatively hyperbolic groups whose law is convergent, in the sense that the derivative of its Green function is finite at the spectral radius.When parabolic subgroups are virtually abelian, we prove that for such a random walk satisfies a local limit theorem of the form $p_n(e, e)\sim CR^{-n}n^{-d/2}$, where $p_n(e, e)$ is the probability of returning to the origin at time $n$, $R$ is the inverse of the spectral radius of the random walk and $d$ is the minimal rank of a parabolic subgroup along which the random walk is spectrally degenerate.This concludes the classification all possible behaviour for $p_n(e, e)$ on such groups.
