本项目致力于随机增长过程的渐近分布理论研究. 特别，着重研究有向聚合模型，不对称单排他交互粒子系统，Dyson布朗运动，Kardar-Parisi-Zhang随机界面增长模型以及它们的变化形式. 主要研究内容：随机增长过程的增长方式，随机波动分布，时-空相关函数以及渐近收敛速度，旨在进一步探索属于KPZ普适性类的更广泛可解模型，并寻求新型分布及随机过程. 主要方法：优化问题中的变差公式，行列式点过程以及二参数核函数的渐近分析，鞅问题求解及收敛性，高阶矩及广义Laplace变换的估计等. 详细分析Tracy-Widom型分布及Airy型过程将在研究中起着关键作用..本项目将努力建立随机增长过程渐近分布理论与统计物理相变、高维随机矩阵谱理论、随机偏微分方程可解性、无穷维对称群表示等领域的联系..随机增长过程是当前概率论中一个十分活跃领域，本项目将为推动该领域在国内的研究和发展做积极贡献。

The project is devoted to the study of asymptotic distribution theory for random growth models. In particular, we focus on a few of solvable models and their variants like directed polymer models, infinite weakly asymmetric simple exclusion interacting particle systems, Dyson Browian motions, Kardar-Parisi-Zhang random growing interface models. Among the main research interests are random growth modes, random fluctuation distributions, time-space correlation functions and the rate of convergence to the limits. The aim is to further dig up more solvable models belonging to the universality classes and look for some new types of limiting distributions and random processes. Main techniques we will use in work are variational formulas for optimization problems, asymptotic analysis for determinantal point processes and two-parameters kernel functions, solving the martingale problems and deciding its convergence, estimations for high moments and generalized Laplace transforms. A refined analysis for Tracy-Widom type distributions and Airy type processes will play a crucial role throughout the project...The project will make many efforts to establish the link between such research fields as asymptotic distribution theory of random growth models and phase transitions in statistical physics, spectral theory of high dimensional random matrices, solvability of nonlinear stochastic partial differential equations, representation theory of infinite dimensional symmetric groups...The study of random growth processes is currently a both hot and active field in probability theory. The present project will hopefully make a remarkably positive contribution to development of such a field around China.