Matrix product construction for Koornwinder polynomials and fluctuations of the current in the open ASEP

Abstract

Starting from the deformed current-counting transition matrix for the open boundary ASEP, we prove that with a further deformation, the symmetric Koornwinder polynomials for partitions with equal row lengths appear as the normalisation of the twice deformed ground state. We give a matrix product construction for this ground state and the corresponding symmetric Koornwinder polynomials. Based on the form of this construction and numerical evidence, we conjecture a relation between the generating function of the cumulants of the current, and a certain limit of the symmetric Koornwinder polynomials.

31 pages

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Cited by in corpus (2)

• Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton
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