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arXiv · 1404.4015

Decorated Young Tableaux and the Poissonized Robinson-Schensted Process

Mihai Nica
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Abstract

We introduce an object called a decorated Young tableau which can equivalently be viewed as a continuous time trajectory of Young diagrams or as a non-intersecting line ensemble. By a natural extension of the Robinson-Schensted correspondence, we create a random pair of decorated Young tableaux from a Poisson point process in the plane, which we think of as a stochastic process in discrete space and continuous time. By using only elementary techniques and combinatorial properties, we identify this process as a Schur process and show it has the same law as certain non-intersecting Poisson walkers.

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Mihai Nica. 2017-03-29. Decorated Young Tableaux and the Poissonized Robinson-Schensted Process. https://doi.org/10.1016/j.spa.2016.06.014

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