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Integrable fluctuations in random growth

With Jeremy Quastel (Toronto)

Integrable fluctuations in random growth

Asymptotic fluctuations in the one dimensional KPZ universality class are governed by a special scaling invariant, completely integrable Markov process, “the KPZ fixed point”. Its transition probabilities are obtained by solving the totally asymmetric simple exclusion process and passing to the limit. The finite dimensional distributions satisfy integrable partial differential equations. We will try to provide a survey without assuming prior knowledge. Joint work with Daniel Remenik and Konstantin Matetsky.

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