We investigate the evolution in time of the position of a fixed number in the insertion tableau when the Robinson–Schensted–Knuth algorithm is applied to a sequence of random numbers. When the length of the sequence tends to infinity, a typical trajectory after scaling converges uniformly in probability to some deterministic curve.

中文翻译：

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Robinson-Schensted-Knuth 算法的流体动力极限

我们研究了当 Robinson-Schensted-Knuth 算法应用于随机数序列时插入表中固定数位置随时间的演变。当序列的长度趋于无穷大时，缩放后的典型轨迹在概率上均匀收敛到某些确定性曲线。