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Stationary Half-space Geometric Last Passage Percolation without Random Shift
Abstract
We derive exact formulas for the diagonal distribution of half-space geometric last-passage percolation with a two-parameter family of stationary initial conditions throughout the phase diagram. Unlike previous results, our formulas remove the random shift at the origin. Under critical scaling, we obtain new formulas for the half-space stationary KPZ fixed-point distribution at x=0 in the high-density and maximal-current phases. In the low-density phase, we derive a new representation and show that it matches the corresponding formula from the stationary log-gamma polymer.
Related
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- Invariance in half-space last passage percolation and directed polymers
- Half-space last passage percolation with inhomogeneous first row
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BibTeX
@misc{occelli2026stationary,
title = {{Stationary Half-space Geometric Last Passage Percolation without Random Shift}},
author = {Alessandra Occelli and Jiyue Zeng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30739},
eprint = {2610.30739},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30739},
}
RIS
TY - UNPB
TI - Stationary Half-space Geometric Last Passage Percolation without Random Shift
AU - Alessandra Occelli
AU - Jiyue Zeng
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30739
UR - https://arxiv.org/abs/2610.30739
AB - We derive exact formulas for the diagonal distribution of half-space geometric last-passage percolation with a two-parameter family of stationary initial conditions throughout the phase diagram. Unlike previous results, our formulas remove the random shift at the origin. Under critical scaling, we obtain new formulas for the half-space stationary KPZ fixed-point distribution at x=0 in the high-density and maximal-current phases. In the low-density phase, we derive a new representation and show that it matches the corresponding formula from the stationary log-gamma polymer.
ER -