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Jeremy Quastel : The Kardar-Parisi-Zhang equation and its universality class

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The KPZ equation was introduced in 1986, and has become the default model in physics for random interface growth. It is a member of a large universality class with non-standard fluctuations, including directed random polymers. Even in one dimension, it turned out to be difficult to interpret and analyze mathematically, but at the same time to have a large degree of exact solvability. We will survey the history and recent progress.

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