弱非对称交互作用粒子系统的标度极限

KPZ普适性是近年来非常活跃的研究领域。某些弱非对称交互作用粒子系统可以帮助人们更好地理解KPZ普适性，因此对其进行深入研究具有十分重要的意义。本项目拟通过大偏差和涨落极限来刻画弱非对称交互作用粒子系统，具体而言：(1)拟利用上指数估计的方法，研究该系统标度变换后经验密度场的大偏差；(2)交互作用粒子系统有无穷多个不变测度，它们的可加泛函的长时间行为表现不能利用马氏过程的一般理论进行研究。拟利用泛函不等式，借助Delta方法及大偏差理论工具研究弱非对称交互作用粒子系统可加泛函的中偏差；(3)通过鞅方法、多分量二阶Boltzmann-Gibbs原理讨论多组分弱非对称交互作用粒子系统密度场的涨落问题。希望通过本项目的研究，可以更深入地理解弱非对称粒子系统的长时间与大尺度行为，进一步拓展KPZ普适性的认识。

The KPZ universality class has been a very active field of research during the past decade. Some weakly asymmetric interacting particle systems help people to get a better understanding of the KPZ universality class. Therefore, it is very significant to intensely study the weakly asymmetric interacting particlesystems. This project will consider large deviations and fluctuations of weakly asymmetric interacting particle systems: (1) Using supexponential estimates, we will study the large deviations for the rescaling empirical density fields of the weakly asymmetric interacting particle systems. (2) Since the interacting particle systems possess a family of invariant measures, long time asymptotics of their additive functionals can not follow from general results of Markov processes. Using functional inequalities, Delta method in moderate deviations and large deviatons techniques, we will establish the moderate deviations for additive functionals of the weakly asymmetric interacting particle systems. (3) By the martingale approach and multi-component Boltzmann-Gibbs principle, we will consider fluctuations for the multi-species weakly asymmetric interacting particle systems. We will comprehend the long time and large scale behavior of the weakly asymmetric interacting particle systems and the KPZ universality conjecture by this project.