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Invariance in half-space last passage percolation and directed polymers
Abstract
We prove various invariance properties for half-space geometric and exponential last passage percolation and the half-space log-gamma polymer, analogous to the full-space invariances proved by Dauvergne. We use the RSK and geometric RSK correspondences to establish a conditional distributional identity between the half-space models and the corresponding full-space models, which allows us to directly transfer the invariance results in the full space to the half space.
Related
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BibTeX
@misc{lou2026invariance,
title = {{Invariance in half-space last passage percolation and directed polymers}},
author = {Yunhao Lou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37694},
eprint = {2610.37694},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37694},
}
RIS
TY - UNPB
TI - Invariance in half-space last passage percolation and directed polymers
AU - Yunhao Lou
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.37694
UR - https://arxiv.org/abs/2610.37694
AB - We prove various invariance properties for half-space geometric and exponential last passage percolation and the half-space log-gamma polymer, analogous to the full-space invariances proved by Dauvergne. We use the RSK and geometric RSK correspondences to establish a conditional distributional identity between the half-space models and the corresponding full-space models, which allows us to directly transfer the invariance results in the full space to the half space.
ER -