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Spectral theory for the q-Boson particle system

Mathematical Physics & Probability

Speaker: Ivan Corwin, Columbia, Clay Mathematics Institute, MIT
Location: 1147 MSB
Start time: Mon, Sep 23 2013, 4:10PM

We develop spectral theory for the generator of the q-Boson particle system. Our central result is a Plancherel type isomorphism theorem for this system. This theorem has various implications. It proves the completeness of the Bethe ansatz for the q-Boson generator and consequently enables us to solve the Kolmogorov forward and backward equations for general initial data. Owing to a Markov duality with q-TASEP, this leads to moment formulas which characterize the fixed time distribution of q-TASEP started from general initial conditions. The theorem also implies the biorthogonality of the left and right eigenfunctions. Some limits of our results relate to directed polymers and the Kardar-Parisi-Zhang equation.