论文标题
奇异相互作用扩散的大偏差
Large deviations for singularly interacting diffusions
论文作者
论文摘要
在本文中，我们证明了对均值场相互作用扩散与单数漂移（因为颗粒的数量倾向于无穷大）的经验度量的大偏差原理（LDP），并显示了与相关的McKean-Vlasov方程的收敛。在此过程中，我们证明了瓦拉达（Varadhan）积分引理的扩展版本，用于不连续的度量变化，随后是吉布斯（Gibbs）和类似吉布斯（Gibbs）的LDP，具有单数电位。
In this paper we prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the associated McKean-Vlasov equation. Along the way, we prove an extended version of the Varadhan Integral Lemma for a discontinuous change of measure and subsequently an LDP for Gibbs and Gibbs-like measures with singular potentials.
