# Dynamic ASEP, duality and continuous $q^{-1}$-Hermite polynomials

@article{Borodin2017DynamicAD, title={Dynamic ASEP, duality and continuous \$q^\{-1\}\$-Hermite polynomials}, author={A. Borodin and I. Corwin}, journal={arXiv: Probability}, year={2017} }

We demonstrate a Markov duality between the dynamic ASEP and the standard ASEP. We then apply this to step initial data, as well as a half-stationary initial data (which we introduce). While investigating the duality for half-stationary initial data, we uncover and utilize connections to continuous $q^{-1}$-Hermite polynomials. Finally, we introduce a family of stationary initial data which are related to the indeterminate moment problem associated with these $q^{-1}$-Hermite polynomials.

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