PreprintCC BY-NC-ND 4.0arXiv
A Stein Proof of the Burke Property for the Stationary O'Connell-Yor Polymer
Abstract
We give a direct proof of the Burke property for the stationary O'Connell-Yor polymer using Stein's method. Building on a free energy identity developed in joint work with Firas Rassoul-Agha, Xiao Shen, and Guangqu Zheng, we establish a multilevel extension that yields a joint Gaussian-Gamma Stein identity, from which the full Burke property follows. The proof is based on a Gaussian integration-by-parts framework developed in that work. Passing to zero temperature gives the corresponding result for stationary point-to-line Brownian last-passage percolation.
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BibTeX
@misc{zhang2026stein,
title = {{A Stein Proof of the Burke Property for the Stationary O'Connell-Yor Polymer}},
author = {Ruixuan Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18214},
eprint = {2609.18214},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18214},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A Stein Proof of the Burke Property for the Stationary O'Connell-Yor Polymer
AU - Ruixuan Zhang
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18214
UR - https://arxiv.org/abs/2609.18214
AB - We give a direct proof of the Burke property for the stationary O'Connell-Yor polymer using Stein's method. Building on a free energy identity developed in joint work with Firas Rassoul-Agha, Xiao Shen, and Guangqu Zheng, we establish a multilevel extension that yields a joint Gaussian-Gamma Stein identity, from which the full Burke property follows. The proof is based on a Gaussian integration-by-parts framework developed in that work. Passing to zero temperature gives the corresponding result for stationary point-to-line Brownian last-passage percolation.
ER -