Lévy-Lorentz气体的大涨落与输运性质
Large fluctuations and transport properties of the Lévy-Lorentz gas
AI总结：
本文研究Lévy-Lorentz气体的大涨落与输运性质，证明退火情形存在超扩散，而淬火典型环境下长时间呈正常扩散。
摘要：
Lévy-Lorentz气体描述了粒子在实轴上、在随机散射点阵列存在时的运动，其中相邻散射点之间的距离是具有有限均值的重尾独立同分布随机变量。该运动是标记点上简单对称随机游走的连续时间、恒定速度插值。本文研究该连续时间过程的大涨落以及模型由此产生的输运性质，分别从退火（annealed）和淬火（quenched）两种情形展开，证实并扩展了物理学家此前关于退火框架的工作。具体而言，我们聚焦于粒子位移，并在散射点间距的尾部分布在无穷远处正则变化的假设下，证明了退火涨落的精确大偏差原理，给出了退火矩的渐近行为，从而展示退火超扩散。随后，我们给出淬火涨落的上大偏差估计以及淬火矩的渐近行为，表明在典型散射点排列条件下的渐近扩散体制是正常扩散，而非超扩散。尽管Lévy-Lorentz气体似乎已被接受为一种反常扩散模型，但我们的发现表明，超扩散是一种瞬态行为，在长时间尺度上会发展为正常扩散；这也提出了一个新问题，即从淬火正常扩散到退火超扩散的转变是如何发生的。
英文摘要：
The Lévy-Lorentz gas describes the motion of a particle on the real line in the presence of a random array of scattering points, whose distances between neighboring points are heavy-tailed i.i.d. random variables with finite mean. The motion is a continuous-time, constant-speed interpolation of the simple symmetric random walk on the marked points. In this paper we study the large fluctuations of the continuous-time process and the resulting transport properties of the model, both annealed and quenched, confirming and extending previous work by physicists that pertain to the annealed framework. Specifically, focusing on the particle displacement, and under the assumption that the tail distribution of the interdistances between scatterers is regularly varying at infinity, we prove a precise large deviation principle for the annealed fluctuations and present the asymptotics of annealed moments, demonstrating annealed superdiffusion. Then, we provide an upper large deviation estimate for the quenched fluctuations and the asymptotics of quenched moments, showing that the asymptotic diffusive regime conditional on a typical arrangement of the scatterers is normal diffusion, and not superdiffusion. Although the Lévy-Lorentz gas seems to be accepted as a model for anomalous diffusion, our findings suggest that superdiffusion is a transient behavior which develops into normal diffusion on long timescales, and raise a new question about how the transition from the quenched normal diffusion to the annealed superdiffusion occurs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
