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Half-space last passage percolation with inhomogeneous first row
Abstract
We consider exponential last passage percolation in half-space with a deterministic first row. This model corresponds to a version of TASEP in half-space in which particles enter at the origin and are restricted by a moving wall. We determine the possible limiting distributions of rescaled last passage times depending on the boundary strength and the choice of the wall. As key inputs to our analysis, we establish several results for point-to-point half-space last passage times, including upper tail bounds, weak convergence, and bounds on the probabilities that geodesics touch the diagonal for certain start and end points.
Related
- Invariance in half-space last passage percolation and directed polymers
- Stationary Half-space Geometric Last Passage Percolation without Random Shift
- Inhomogeneous Long-Range First-Passage Percolation in a Random Vertex Environment
- Inhomogeneous Geometric Last Passage Percolation and the q-deformed Jacobi Unitary Ensemble
- Fluctuation bounds for rotationally invariant first-passage percolation
BibTeX
@misc{ferrari2026halfspace,
title = {{Half-space last passage percolation with inhomogeneous first row}},
author = {Patrik L. Ferrari and Sabrina Gernholt},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21413},
eprint = {2610.21413},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21413},
}
RIS
TY - UNPB
TI - Half-space last passage percolation with inhomogeneous first row
AU - Patrik L. Ferrari
AU - Sabrina Gernholt
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21413
UR - https://arxiv.org/abs/2610.21413
AB - We consider exponential last passage percolation in half-space with a deterministic first row. This model corresponds to a version of TASEP in half-space in which particles enter at the origin and are restricted by a moving wall. We determine the possible limiting distributions of rescaled last passage times depending on the boundary strength and the choice of the wall. As key inputs to our analysis, we establish several results for point-to-point half-space last passage times, including upper tail bounds, weak convergence, and bounds on the probabilities that geodesics touch the diagonal for certain start and end points.
ER -