The transition probability and the probability for the left-most particle's position of the q-TAZRP
The transition probability and the probability for the left-most particle's position of the q-TAZRP
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DOI：
10.1063/1.4851758
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发表时间：
2013-08
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通讯作者：
Marko Korhonen;Eunghyun Lee
中科院分区：
文献类型：
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作者：
Marko Korhonen;Eunghyun Lee
我们处理跳跃率满足一定条件的N粒子ZRP。这一条件是使用Bethe ansatz所必需的，所得到的模型是出现在[J.Phys.31 6057-6071(1998)]Sasamoto和Wadati或Q-TAZRP in Macdonald Procedure由Borodin和Corwin提出。我们通过Bethe ansatz得到了Q-TAZRP跃迁几率的显式公式。通过使用跃迁概率，我们得到了最左边粒子在时间t的位置的概率分布。为了找到最左边粒子位置的概率，我们找到了一个新的恒等式，对应于Tracy和Widom在[Commun]中的Asep恒等式。数学课。物理，279815-844(2008)]。对于所有粒子占据一个位置的初始状态，最左侧粒子在时间t的位置的概率分布用行列式的轮廓积分来表示。
We treat the N-particle ZRP whose jumping rates satisfy a certain condition. This condition is required to use the Bethe ansatz and the resulting model is the q-boson model that appeared in [J. Phys. A, 31 6057–6071 (1998)] by Sasamoto and Wadati or the q-TAZRP in Macdonald processes by Borodin and Corwin. We find the explicit formula of the transition probability of the q-TAZRP via the Bethe ansatz. By using the transition probability we find the probability distribution of the left-most particle’s position at time t. To find the probability for the left-most particle’s position we find a new identity corresponding to Tracy and Widom’s identity for the ASEP in [Commun. Math. Phys., 279 815–844 (2008)]. For the initial state that all particles occupy a single site, the probability distribution of the left-most particle’s position at time t is represented by the contour integral of a determinant.