Conditional Flat Exponential Directed Last Passage Percolation under a One-Point Upper Large Deviation Event
Abstract
Exponential directed last passage percolation is a random maximization model connected to tandem queues and interacting particle systems. We study the line-to-point model of the percolation, in which the starting point is allowed to vary inside a line boundary, conditioned on an atypically large last-passage time to a fixed endpoint. Extending recent results for the point-to-point model where the starting point is fixed, we develop heuristic predictions for the conditional limit shape and prove corresponding fluctuation results in certain regimes through steepest-descent analysis of exact multi-point formulas. Our calculations suggest that the conditional fluctuations near diagonal are described by Brownian bridges coupled through an additional shared Gaussian component.
Related
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BibTeX
@misc{dadlani2026conditional,
title = {{Conditional Flat Exponential Directed Last Passage Percolation under a One-Point Upper Large Deviation Event}},
author = {Rishi Dadlani and Shaotian Sun},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09018},
eprint = {2610.09018},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09018},
}
RIS
TY - UNPB
TI - Conditional Flat Exponential Directed Last Passage Percolation under a One-Point Upper Large Deviation Event
AU - Rishi Dadlani
AU - Shaotian Sun
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.09018
UR - https://arxiv.org/abs/2610.09018
AB - Exponential directed last passage percolation is a random maximization model connected to tandem queues and interacting particle systems. We study the line-to-point model of the percolation, in which the starting point is allowed to vary inside a line boundary, conditioned on an atypically large last-passage time to a fixed endpoint. Extending recent results for the point-to-point model where the starting point is fixed, we develop heuristic predictions for the conditional limit shape and prove corresponding fluctuation results in certain regimes through steepest-descent analysis of exact multi-point formulas. Our calculations suggest that the conditional fluctuations near diagonal are described by Brownian bridges coupled through an additional shared Gaussian component.
ER -