论文标题
局部极限定理中的急剧误差项，并混合洛伦兹气体与无限的地平线
Sharp error term in local limit theorems and mixing for Lorentz gases with infinite horizon
论文作者
论文摘要
我们在Sinai台球地图（一维台球图）的局部极限定理中获得了急剧错误率，该错误率具有无限的地平线。这一结果使我们能够进一步获得更高的术语，因此，在地图（离散时间）情况下，在平面和管状无限的地平线洛伦兹气体（离散时间）中，动态Hölder可观察物的混合速度的急剧混合速率。我们还获得了第一次回归初始单元的尾巴概率的渐近估计。在此过程中，我们研究了转移操作员的家族，用于无限的西奈台球台球，并扰乱了自由飞行功能，并为特征值和本征局体的相关家族获得了更高阶的扩张。
We obtain sharp error rates in the local limit theorem for the Sinai billiard map (one and two dimensional) with infinite horizon. This result allows us to further obtain higher order terms and thus, sharp mixing rates in the speed of mixing of dynamically Hölder observables for the planar and tubular infinite horizon Lorentz gases in the map (discrete time) case. We also obtain an asymptotic estimate for the tail probability of the first return time to the initial cell. In the process, we study families of transfer operators for infinite horizon Sinai billiards perturbed with the free flight function and obtain higher order expansions for the associated families of eigenvalues and eigenprojectors.
