The One-Dimensional KPZ Equation and Its Universality Class

Abstract

Our understanding of the one-dimensional KPZ equation, alias noisy Burgers equation, has advanced substantially over the past 5 years. We provide a non-technical review, where we limit ourselves to the stochastic PDE and lattice type models approximating it.

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Acknowledgments

We are grateful for the generous hospitality at the Institute for Advanced Study, Princeton, where the first draft was written when both of us participated in the special year on “Non-equilibrium Dynamics and Random Matrices”. We thank Patrik Ferrari for help with the figures.

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Correspondence to Herbert Spohn.

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Quastel, J., Spohn, H. The One-Dimensional KPZ Equation and Its Universality Class. J Stat Phys 160, 965–984 (2015). https://doi.org/10.1007/s10955-015-1250-9

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Keywords

  • Exact solutions
  • Approximating lattice type models
  • Replicas