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2022 RSK in last passage percolation: a unified approach
Duncan Dauvergne, Mihai Nica, Bálint Virág
Author Affiliations +
Probab. Surveys 19: 65-112 (2022). DOI: 10.1214/22-PS4

Abstract

We present a version of the RSK correspondence based on the Pitman transform and geometric considerations. This version unifies ordinary RSK, dual RSK and continuous RSK. We show that this version is both a bijection and an isometry, two crucial properties for taking limits of last passage percolation models.

We use the bijective property to give a non-computational proof that dual RSK maps Bernoulli walks to nonintersecting Bernoulli walks.

Funding Statement

D.D. and M.N. were supported by NSERC postdoctoral fellowships. B.V. was supported by the Canada Research Chair program and an NSERC Discovery Accelerator Grant.

Citation

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Duncan Dauvergne. Mihai Nica. Bálint Virág. "RSK in last passage percolation: a unified approach." Probab. Surveys 19 65 - 112, 2022. https://doi.org/10.1214/22-PS4

Information

Received: 1 June 2021; Published: 2022
First available in Project Euclid: 7 March 2022

Digital Object Identifier: 10.1214/22-PS4

Subjects:
Primary: 05A05
Secondary: 60K35

Keywords: Greene’s theorem , KPZ universality class , Last passage percolation , Pitman transform , Robinson-Schensted correspondence , RSK bijection , Young tableaux

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