KPZ普适性以及Tracy-Widom律是近些时间才发展起来一个重要的研究领域。基于我们的研究特色，在此项目中我们集中研究交互粒子系统的大刻度极限、长时间行为和自由能的渐近性质，特别地研究相应的大偏差和中偏差理论。同时我们也研究各种随机游动在（时间或空间）相依随机环境影响下其自由能的KPZ普适性和Tracy-Widom律以及相应的KPZ方程的极限分布。我们希望通过对该项目的研究能对KPZ普适类和Tracy-Widom律的发展作出重要的贡献。

KPZ Universality and Tracy-Widom law are important fields developed recently. Based on our past research we propose this project, in which we will be concentrated on the study of large scaling limits and long time behaviors of interacting particle systems, and asymptotic properties of free energy, especially in the study of large deviations and moderate deviations. Also we are focused on finding some new KPZ universality of free energy of random walks in terms of all kinds of fluctuation exponents when they are placed in the random environment. Especially we look for the limit distribution of corresponding KPZ equations in the time or spatial correlated random environment. We are expected to make some contributions on the development of KPZ universality and Tracy-Widom law.