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An interacting particle system related to the quantum Toda chain

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Mathematics and Physics of Anderson localization: 50 Years After

I will describe an interacting particle system which can be `solved’ via a connection with the quantum Toda chain. The particle system can be regarded as a discretisation of the KPZ (or stochastic heat) equation and is closely related to a semi-discrete directed random polymer model in 1+1 dimensions. The connection to the quantum Toda chain yields an explicit integral formula for the Laplace transform of the distribution of the partition function associated with the polymer model.

This talk is part of the Isaac Newton Institute Seminar Series series.

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