无限Young tableaux和第二类粒子上的Jeu de Taquin动力学
Jeu de taquin dynamics on infinite Young tableaux and second class particles
摘要：
我们研究了一个无限版本的“jeu de taquin”滑动游戏，它可以被认为是一个自然的保测变换的集合上的无限杨tableaux配备Plancherel概率测度。我们使用表示论的方法表明，Robinson-Schensted-Knuth（$\operatorname {RSK}$）算法给出了一个同构之间的测度保持动力系统和单侧移位动力学的序列上的独立和同分布的随机变量均匀分布的单位区间。我们还证明了由变换诱导的jeu de taquin轨迹是从原点沿随机方向发出的渐近直线，其分布被显式计算，并表明这一结果可以解释为Plancherel-TASEP粒子系统中第二类粒子的极限速度的陈述（与Plancherel增长相关的完全不对称简单排它过程的变体），与普通TASEP中第二类粒子的早期结果类似。
英文摘要：
We study an infinite version of the "jeu de taquin" sliding game, which can be thought of as a natural measure-preserving transformation on the set of infinite Young tableaux equipped with the Plancherel probability measure. We use methods from representation theory to show that the Robinson-Schensted-Knuth ($\operatorname {RSK}$) algorithm gives an isomorphism between this measure-preserving dynamical system and the one-sided shift dynamics on a sequence of independent and identically distributed random variables distributed uniformly on the unit interval. We also show that the jeu de taquin paths induced by the transformation are asymptotically straight lines emanating from the origin in a random direction whose distribution is computed explicitly, and show that this result can be interpreted as a statement on the limiting speed of a second-class particle in the Plancherel-TASEP particle system (a variant of the Totally Asymmetric Simple Exclusion Process associated with Plancherel growth), in analogy with earlier results for second class particles in the ordinary TASEP.
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