Summary.
The study of the Burgers equation with a random force leads via a Hopf-Cole type transformation to a stochastic heat equation having a white noise with spatial parameters type potential. The latter can be studied by means of a general model of directed polymers in random environments with two point random potentials. These models exhibit a Gaussian behavior at large times and have certain stationary distributions which yield the corresponding results for the above stochastic heat and Burgers equations.
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Received: 18 July 1995 / In revised form: 5 August 1995
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Kifer, Y. The Burgers equation with a random force and a general model for directed polymers in random environments. Probab Theory Relat Fields 108, 29–65 (1997). https://doi.org/10.1007/s004400050100
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DOI: https://doi.org/10.1007/s004400050100