论文标题
Kontsevich-Zorich Cocycle的中心限制定理
A Central Limit Theorem for the Kontsevich-Zorich Cocycle
论文作者
论文摘要
我们表明，中央限制定理具有Kontsevich-Zorich（Kz）Cocycle的外部力量。特别是，我们表明，在假设外部力量上的最高lyapunov指数很简单，中心限制定理可将（叶轮）双曲线布朗尼运动提高到任何难以简易的，simplectic，$ \ text {sl}（2，2，\ nathbb {r}）$ - novariant symelt--所谓的重言式分支。然后，我们表明这意味着中央限制定理将Teichmüller测量流到同一束的升降。 对于双曲线布朗尼运动上的随机合过程，我们在相同的假设下证明了顶部指数的方差严格是阳性的。对于Teichmüller测量流的确定性共生，我们证明，在其Lyapunov Spectrum很简单的假设下，方差仅对第一个外部力量（KZ Cocycle本身）的顶部指数（Kz Cocycle本身）是严格的。
We show that a central limit theorem holds for exterior powers of the Kontsevich-Zorich (KZ) cocycle. In particular, we show that, under the hypothesis that the top Lyapunov exponent on the exterior power is simple, a central limit theorem holds for the lift of the (leafwise) hyperbolic Brownian motion to any strongly irreducible, symplectic, $\text{SL}(2,\mathbb{R})$-invariant subbundle, that is moreover symplectic-orthogonal to the so-called tautological subbundle. We then show that this implies that a central limit theorem holds for the lift of the Teichmüller geodesic flow to the same bundle. For the random cocycle over the hyperbolic Brownian motion, we prove under the same hypotheses that the variance of the top exponent is strictly positive. For the deterministic cocycle over the Teichmüller geodesic flow we prove that the variance is strictly positive only for the top exponent of the first exterior power (the KZ cocycle itself) under the hypothesis that its Lyapunov spectrum is simple.
