The oriented swap process.
The oriented swap process.
复制标题
定向交换过程。
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
D. Romik
中科院分区：
文献类型：
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作者：
Omer Angel;A. Holroyd;D. Romik
标记为1，...，n最初以递增的顺序排列。随后，当前处于递增顺序的每对相邻粒子根据速率为1的泊松过程交换。我们分析了这个过程的渐近行为n → oo。我们证明了单个粒子的时空轨迹收敛（当适当缩放时）到具有两个不可微点的某个随机曲线族，并且在给定时间的置换矩阵收敛到具有绝对连续和奇异部分的某个确定性测度。在时间（2 + o（1））n处达到吸收状态（其中所有粒子按降序排列）。单个粒子的完成时间收敛到确定性极限，波动渐近地由Tracy-Widom分布控制。
Particles labelled 1, ..., n are initially arranged in increasing order. Subsequently, each pair of neighboring particles that is currently in increasing order swaps according to a Poisson process of rate 1. We analyze the asymptotic behavior of this process as n → oo. We prove that the space―time trajectories of individual particles converge (when suitably scaled) to a certain family of random curves with two points of non-differentiability, and that the permutation matrix at a given time converges to a certain deterministic measure with absolutely continuous and singular parts. The absorbing state (where all particles are in decreasing order) is reached at time (2 + o(1))n. The finishing times of individual particles converge to deterministic limits, with fluctuations asymptotically governed by the Tracy―Widom distribution.