论文标题
相互作用的多尺寸粒子系统的大偏差
Large deviations for interacting multiscale particle systems
论文作者
论文摘要
我们考虑在两个局部周期性环境中移动的弱相互作用扩散过程的集合。我们研究了粒子位置的经验分布在合并极限下的大偏差原理，因为粒子的数量生长到无穷大，并且时间尺度的分离参数同时为零。我们利用弱收敛方法为大偏差率函数提供方便的表示，这使我们能够表征有效的受控平均场动力学。此外，我们还获得了Dawson-Gärtner形式的大偏差速率函数的等效表示，即使在扩散矩阵取决于经验度量以及粒子在混乱的传播之外进行平均的情况下，该形式仍然存在。
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit as the number of particles grow to infinity and the time-scale separation parameter goes to zero simultaneously. We make use of weak convergence methods providing a convenient representation for the large deviations rate function, which allow us to characterize the effective controlled mean field dynamics. In addition, we obtain equivalent representations for the large deviations rate function of the form of Dawson-Gärtner which hold even in the case where the diffusion matrix depends on the empirical measure and when the particles undergo averaging in addition to the propagation of chaos.
