Dynamic ASEP, Duality, and Continuous q−1-Hermite Polynomials
Dynamic ASEP, Duality, and Continuous q−1-Hermite Polynomials
复制标题
动态 ASEP、对偶性和连续 q-1-Hermite 多项式
DOI：
10.1093/imrn/rnx299
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发表时间：
2018
影响因子：
1
通讯作者：
Corwin, Ivan
中科院分区：
文献类型：
--
作者：
Borodin, Alexei;Corwin, Ivan
我们证明了动态非对称简单排除过程（ASEP）和标准ASEP之间的马尔可夫对偶。然后，我们将其应用于步骤初始数据，以及半稳态初始数据（我们引入）。在研究半平稳初始数据的对偶性时，我们发现并利用了与连续q −1-Hermite多项式的联系。最后，我们介绍了一个家庭的平稳的初始数据，这是有关的不定矩问题与theseq-1-Hermite多项式。
We demonstrate a Markov duality between the dynamic asymmetric simple exclusion process (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 the continuousq−1-Hermite polynomials. Finally, we introduce a family of stationary initial data which are related to the indeterminate moment problem associated with theseq−1-Hermite polynomials.