竞争界面的粗糙化和倾斜
Roughening and inclination of competition interfaces
摘要：
二维随机锥中两个成长中的“Young团簇”（图）之间的竞争界面映射为一维完全非对称简单排它过程中第二类粒子的路径.利用排它过程（Burgers方程）的第二类粒子和流体力学极限的渐近性，我们证明了竞争界面的行为依赖于锥角：对于[180 ^o，270 ^o）的锥角，竞争界面具有确定的倾角，而对于[90 ^o，180 ^o）的锥角，竞争界面的倾角是随机的.我们将竞争模型与无规定向聚合物模型联系起来，得到了竞争界面涨落的部分结果。
英文摘要：
The competition interface between two growing ``Young clusters'' (diagrams), in a two-dimensional random cone, is mapped to the path of a second-class particle in the one-dimensional totally asymmetric simple exclusion process. Using the asymptotics of the second class particle and hydrodynamic limits for the exclusion process (Burgers equation), we show that the behavior of the competition interface depends on the angle of the cone: for angles in [180^o, 270^o) the competition interface has a deterministic inclination, while for angles in [90^o,180^o) the inclination is random. We relate the competition model to a model of random directed polymers, and obtain some partial results for the fluctuations of the competition interface.
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