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}
}
  • A. Borodin, I. Corwin
  • Published 2017
  • Mathematics, Physics
  • arXiv: Probability
  • 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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