Dynamic ASEP, Duality, and Continuous q[superscript -1]-Hermite Polynomials

Abstract

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[superscript -1]-Hermite polynomials. Finally, we introduce a family of stationary initial data which are related to the indeterminate moment problem associated with these q[superscript -1]-Hermite polynomials.