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This is a Quantitative Study study.

October 10, 2025Open Access

A note on last passage percolation and Schur processes

Puntos clave

Last passage percolation with geometric weights aligns with Schur processes under specific conditions.
A general proof demonstrates the equality in both full-space and half-space settings.
Key ingredients include generalizations of the Robinson-Schensted-Knuth correspondence and Greene's theorem.
Fomin's growth diagrams serve as a foundational element in establishing the proof.

Resumen

In this note we provide a short proof of the distributional equality between last passage percolation with geometric weights along a general down-right path and Schur processes. We do this in both the full-space and half-space settings, and for general parameters. The main inputs for our arguments are generalizations of the Robinson-Schensted-Knuth correspondence and Greene's theorem due to Krattenthaler, which are based on Fomin's growth diagrams.

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Cite This Study

Dimitrov et al. (Mon,) studied this question.

synapsesocial.com/papers/68e997abe14057276da7f1ee https://doi.org/https://doi.org/10.48550/arxiv.2510.04713