Robinson-Schensted对应和多线Hammersley过程的Poisson极限定理
Poisson limit theorems for the Robinson-Schensted correspondence and for the multi-line Hammersley process
摘要：
考虑Robinson-Schensted-Knuth算法应用于随机输入，并研究了相应Young图底部行的增长性。我们证明多维泊松极限定理的Plancherel增长过程。通过这种方式，我们将Aldous和Diaconis的结果推广到不止一行。这个结果可以解释为多线Hammersley过程收敛到由独立Poisson点过程的集合给出的平稳分布。
英文摘要：
We consider Robinson-Schensted-Knuth algorithm applied to a random input and study the growth of the bottom rows of the corresponding Young diagrams. We prove multidimensional Poisson limit theorem for the resulting Plancherel growth process. In this way we extend the result of Aldous and Diaconis to more than just one row. This result can be interpreted as convergence of the multi-line Hammersley process to its stationary distribution which is given by a collection of independent Poisson point processes.
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