Ergodic-theoretical study of dynamical systems and stochastic processes related to the theory of Teichmuller spaces

对于我们先前研究中得到的“TeichMuller布朗运动”的候选者，我们证明了它的跃迁几率密度满足一些有用的不等式。不幸的是，我们并没有成功到可以建立其固有度量与Teichmuller度量之间的显式关系。另一方面，对于重整化的Ruazy-Veech-Zorich归纳法，我们得到了一个结果，证明了Chebotarev型密度定理对映射类群的双曲元素分布的有效性。

For the candidate of the "Teichmuller Brownian motion" obtained in our preceding research, we show that its transition probability densities satisfy some useful inequalities. Unfortunately, we are not so successful that we can establish the explicit relation of its intrinsic metric with the Teichmuller metric. On the other hand, for the renormalized Ruazy-Veech-Zorich induction, we obtain a result that illustrates the validity of Chebotarev type density theorem for the distribution of hyperbolic elements of the mapping class group.