Competition interfaces and second class particles
Competition interfaces and second class particles
复制标题
竞争接口和二级粒子
DOI：
10.1214/009117905000000080
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发表时间：
2004
影响因子：
2.3
通讯作者：
Leandro P. R. Pimentel
中科院分区：
文献类型：
--
作者：
P. Ferrari;Leandro P. R. Pimentel
一维最近邻完全不对称简单不相容过程可以在与z2中最后通道渗流模型相同的空间中构造。我们证明了在最后通道渗流模型中，第二类粒子在排斥过程中的轨迹可以线性映射到两个生长簇之间的竞争界面。利用在渗流中建立的测地线技术，我们证明了竞争界面几乎肯定地收敛于一个渐进随机方向。由此，我们得到了稀薄扇中第二类粒子强大数定律的一个新的证明，并描述了竞争界面渐近角的分布。
The one-dimensional nearest-neighbor totally asymmetric simple exclusion process can be constructed in the same space as a last-passage percolation model in Z 2 . We show that the trajectory of a second class particle in the exclusion process can be linearly mapped into the competition interface between two growing clusters in the last-passage percolation model. Using technology built up for geodesics in percolation, we show that the competition interface converges almost surely to an asymptotic random direction. As a consequence we get a new proof for the strong law of large numbers for the second class particle in the rarefaction fan and describe the distribution of the asymptotic angle of the competition interface.