LIL for the Length of the Longest Increasing Subsequences  

作　　者：Zhong-gen SU 

机构地区：[1]School of Mathematcial Sciences,Zhejiang University,Hangzhou 310027,China

出　　处：《Acta Mathematicae Applicatae Sinica》2020年第2期283-293,共11页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11871425,11731012);the Fundamental Research Funds for Central Universities.

摘　　要：Let X1,X2,…,Xn,…be a sequence of i.i.d.random variables uniformly distributed on[0;1],and denote by Ln the length of the longest increasing subsequences of X1,X2,…,Xn.Consider the poissonized version Hn based on Hammersley’s representation in the 2-dimensional space.A law of the iterated logarithm for Hn is established using the well-known subsequence method and Borel-Cantelli lemma.The key technical ingredients in the argument include superadditivity,increment independence and precise tail estimates for the Hn’s.The work was motivated by recent works due to Ledoux(J.Theoret.Probab.31,(2018)).It remains open to establish an analog for the Ln itself.

关 键 词：Borel-Cantelli LEMMA Hammersley's representation law of the ITERATED LOGARITHM longest INCREASING SUBSEQUENCES 

分 类 号：O211.5[理学—概率论与数理统计]