We consider the stationary O'Connell-Yor model of semi-discrete directed polymers in a Brownian environment in the intermediate disorder regime and show convergence of the increments of the log-partition function to the energy solutions of the stochastic Burgers equation. The proof does not rely on the Cole-Hopf transform and avoids the use of spectral gap estimates for the discrete model. The key technical argument is a second-order Boltzmann-Gibbs principle.

中文翻译：

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Burgers 方程的固定定向聚合物和能量解

我们考虑在布朗环境中处于中间无序状态的半离散定向聚合物的平稳 O'Connell-Yor 模型，并显示对数分配函数的增量收敛到随机 Burgers 方程的能量解。该证明不依赖于 Cole-Hopf 变换，并且避免了对离散模型使用谱间隙估计。关键的技术参数是二阶玻尔兹曼-吉布斯原理。