Towards KPZ universality

This will be a survey talk on asymptotic fluctuations in the KPZ universality class.  These are governed by an invariant fixed point whose transition probabilities are given by determinants and satisfy integrable partial differential equations. Convergence to the fixed point of some non-integrable models like the KPZ equation and partially asymmetric exclusions is obtained by comparison with the integrable case using energy estimates.

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