The $q$-Hahn PushTASEP
The $q$-Hahn PushTASEP
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$q$-Hahn PushTASEP
DOI：
10.1093/imrn/rnz106
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发表时间：
2019
影响因子：
1
通讯作者：
Petrov, Leonid
中科院分区：
文献类型：
--
作者：
Corwin, Ivan;Matveev, Konstantin;Petrov, Leonid
我们介绍了哈恩PushTASEP-一个可积的随机相互作用粒子系统，这是一个三参数推广的PushTASEP，一个著名的近亲的TASEP（完全不对称简单排斥过程）。Hahn PushTASEP中的跃迁几率用基本超几何函数表示。在适当的限制下，Hahn PushTASEP退化为所有已知的可积的（1+1）维随机系统的推动机制。因此，人们可以将我们的新系统视为Povolotsky引入的Hahn TASEP的推动对应物。我们建立马尔可夫对偶关系和轮廓积分公式的哈恩PushTASEP。在我们的过程中，我们到达一个随机递归，这在一个特殊的情况下，似乎是类似的逆β聚合物模型。然而，与Beta聚合物模型的递归不同，权重（即，递归的系数）以非平凡的方式依赖于配分函数的先前值。
We introduce the-Hahn PushTASEP—an integrable stochastic interacting particle system that is a three-parameter generalization of the PushTASEP, a well-known close relative of the TASEP (totally asymmetric simple exclusion process). The transition probabilities in the-Hahn PushTASEP are expressed through thebasic hypergeometric function. Under suitable limits, the-Hahn PushTASEP degenerates to all known integrable (1+1)-dimensional stochastic systems with a pushing mechanism. One can thus view our new system as a pushing counterpart of the-Hahn TASEP introduced by Povolotsky . We establish Markov duality relations and contour integral formulas for the-Hahn PushTASEP. In alimit of our process we arrive at a random recursion, which, in a special case, appears to be similar to the inverse-Beta polymer model. However, unlike in recursions for Beta polymer models, the weights (i.e., the coefficients of the recursion) in our model depend on the previous values of the partition function in a nontrivial manner.