AI 中文总结
研究基于无限RSK对应产生的普兰切尔随机无限杨表格的逆映射，利用推盘森林这一未探索结构给出其明确几何特征，证明森林中树的延伸性质并建立双射，通过树寿命恢复顺序。
AI 中文摘要
普兰切尔随机无限杨表格源于将无限罗宾逊 - 施肯斯泰德 - 克努特（RSK）对应应用于在单位区间[0,1]上均匀分布的独立同分布随机变量序列。基于先前工作中建立的动力系统同构，我们给出了逆映射的明确几何特征。我们的方法利用了无限表格上以前未探索的结构——推盘森林，其中边根据局部比较规则连接框。我们证明了该森林中的每棵树几乎必然以明确的渐近方向延伸至无穷，在树与独立同分布输入序列中的值之间建立了规范双射。通过迭代推盘变换下的树寿命恢复顺序。
英文摘要
The Plancherel-random infinite Young tableau arises from applying the infinite Robinson-Schensted-Knuth (RSK) correspondence to a sequence of i.i.d. random variables distributed uniformly on the unit interval [0,1]. Building on the isomorphism of dynamical systems established in prior work, we provide an explicit geometric characterization of the inverse map. Our approach makes use of a previously unexplored structure, the jeu de taquin forest on the infinite tableau, where edges connect boxes according to local comparison rules. We prove that each tree in this forest almost surely extends toward infinity with a well-defined asymptotic direction, establishing a canonical bijection between trees and values in the i.i.d. input sequence. The ordering is recovered through tree lifetimes under iterated jeu de taquin transformations.
Comments34 pages, 10 figures
