Abstract

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.