Fluctuations for stationary q-TASEP
Fluctuations for stationary q-TASEP
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DOI：
10.1007/s00440-018-0868-3
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发表时间：
2018-09
影响因子：
2
通讯作者：
T. Imamura;T. Sasamoto
中科院分区：
文献类型：
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作者：
T. Imamura;T. Sasamoto
本文考虑q-完全非对称简单排斥过程（q-TASEP）在定态区的情形，研究了粒子位置的涨落。我们首先观察到，该问题可以作为一个极限情况下的anN-particleq-TASEP与随机初始条件和粒子依赖的跳跃率进行研究。然后，我们解释了这个N粒子q-TASEP如何被编码到由双边dq-Whittaker过程描述的双边Gelfand-Tsetlin锥上的动力学中，并给出了粒子位置的q-Laplace变换的Fredholm行列式公式。在其推导过程中的两个主要成分是拉马努金的双边求和公式和柯西行列式恒等式的theta函数与一个额外的参数。在此基础上，我们建立了一个粒子的位置服从普适平稳KPZ分布（Baik-Rains分布）在长时间的限制。
We consider theq-totally asymmetric simple exclusion process (q-TASEP) in the stationary regime and study the fluctuation of the position of a particle. We first observe that the problem can be studied as a limiting case of anN-particleq-TASEP with a random initial condition and with particle dependent hopping rate. Then we explain how thisN-particleq-TASEP can be encoded in a dynamics on a two-sided Gelfand–Tsetlin cone described by a two-sidedq-Whittaker process and present a Fredholm determinant formula for theq-Laplace transform of the position of a particle. Two main ingredients in its derivation is the Ramanujan’s bilateral summation formula and the Cauchy determinant identity for the theta function with an extra parameter. Based on this we establish that the position of a particle obeys the universal stationary KPZ distribution (the Baik–Rains distribution) in the long time limit.