平稳O'Connell-Yor聚合物的Burke性质的Stein证明
A Stein Proof of the Burke Property for the Stationary O'Connell-Yor Polymer
- University of Utah（犹他大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文用Stein方法直接证明了平稳O'Connell-Yor聚合物的Burke性质，通过多水平扩展建立联合高斯-伽马Stein恒等式，并推广到零温度情形。
AI中文摘要：
我们利用Stein方法给出了平稳O'Connell-Yor聚合物的Burke性质的直接证明。基于与Firas Rassoul-Agha、Xiao Shen和Guangqu Zheng合作研究中发展的自由能恒等式，我们建立了一个多水平扩展，产生了一个联合高斯-伽马Stein恒等式，完整的Burke性质由此得出。该证明基于该工作中发展的高斯分部积分框架。通过将温度降至零，我们得到了平稳点到线布朗末次通过渗流的相应结果。
英文摘要：
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.
