论文标题
圈子中的随机台球地图
A Random Billiard Map in the Circle
论文作者
论文摘要
我们考虑一个随机的台球图，其中标准镜面反射规则被马尔可夫操作员给出的随机反射所取代。我们在一般表上展示了随机台球的不变措施。在圆形桌子的特殊情况下，我们表明几乎每个（随机）轨道在边界以及圆边界和随机苛性碱之间形成的圆环中密集。我们还证明了针对liouville的绝对连续措施的特定案例，这是强大的克努森定律。
We consider a random billiard map, the one in which the standard specular reflection rule is replaced by a random reflection given by a Markov operator. We exhibit an invariant measure for random billiards on general tables. In the special case of a circular table we show that almost every (random) orbit is dense in the boundary as well as in the circular ring formed between the circle boundary and the random caustic. We additionally prove Strong Knudsen's Law for a particular case of families of absolutely continuous measures with respect to Liouville.
