引力场中变密度洛伦兹气体的随机飞行过程
A random flight process associated to a Lorentz gas with variable density in a gravitational field
摘要：
我们研究了随机飞行过程中出现的玻尔兹曼-格拉德极限的随机散射洛伦兹气体与可变散射密度的引力场。对于幂函数密度，我们展示了模型的参数如何确定轨迹的垂直分量的递归或瞬态。最后，我们的方法表明，适当的缩放空间，时间和密度的障碍物，粒子的轨迹收敛到一个扩散与明确给定的参数。
英文摘要：
We investigate the random flight process that arises as the Boltzmann-Grad limit of a random scatterer Lorentz gas with variable scatterer density in a gravitational field. For power function densities we show how the parameters of the model determine recurrence or transience of the vertical component of the trajectory. Finally, our methods show that, with appropriate scaling of space, time and the density of obstacles, the trajectory of the particle converges to a diffusion with explicitly given parameters.
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