稠密谱极限下$\cN$粒子随机加速的高斯收敛性
Gaussian convergence for stochastic acceleration of $\cN$ particles in the dense spectrum limit
摘要：
在具有独立复振幅的稠密波谱的极限下，一维波场中的被动粒子速度收敛于Wiener过程，其中随机相位分布模$π/2$不变，功率谱期望是均匀的.证明提供了一个完整的概率基础，拟线性近似在此限制。结果扩展到任意数量的粒子，发现使用的合奏图片为他们的行为在一个单一的实现的随机波场。
英文摘要：
The velocity of a passive particle in a one-dimensional wave field is shown to converge in law to a Wiener process, in the limit of a dense wave spectrum with independent complex amplitudes, where the random phases distribution is invariant modulo $π/2$ and the power spectrum expectation is uniform. The proof provides a full probabilistic foundation to the quasilinear approximation in this limit. The result extends to an arbitrary number of particles, founding the use of the ensemble picture for their behaviour in a single realization of the stochastic wave field.
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。
