A Stein Proof of the Burke Property for the Stationary O'Connell-Yor Polymer

RESUMO

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.