Stationary Directed Polymers and Energy Solutions of the Burgers Equation

Milton Jara; Gregorio R. Moreno Flores

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arXiv · 1908.06591

Stationary Directed Polymers and Energy Solutions of the Burgers Equation

Milton Jara·Gregorio R. Moreno Flores

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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.

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Milton Jara, Gregorio R. Moreno Flores. 2019-08-16. Stationary Directed Polymers and Energy Solutions of the Burgers Equation. https://arxiv.org/abs/1908.06591

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