Dynamic ASEP, duality and continuous $q^{1}$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 halfstationary initial data (which we introduce). While investigating the duality for halfstationary 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2017
 arXiv:
 arXiv:1705.01980
 Bibcode:
 2017arXiv170501980B
 Keywords:

 Mathematics  Probability;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 Mathematics  Combinatorics
 EPrint:
 18 pages, 2 figures