Koornwinder多项式的矩阵积构造和开放式ASEP中电流的波动
Matrix product construction for Koornwinder polynomials and fluctuations of the current in the open ASEP
摘要：
从变形的电流计数转移矩阵的开放边界的ASEP，我们证明，与进一步的变形，对称Koornwinder多项式的分区具有相等的行长度出现作为两次变形的基态的归一化。我们给出了这个基态的矩阵乘积结构和相应的对称Koornwinder多项式。基于这种构造的形式和数值证据，我们推测了电流累积量的母函数与对称Koornwinder多项式的一定极限之间的关系。
英文摘要：
Starting from the deformed current-counting transition matrix for the open boundary ASEP, we prove that with a further deformation, the symmetric Koornwinder polynomials for partitions with equal row lengths appear as the normalisation of the twice deformed ground state. We give a matrix product construction for this ground state and the corresponding symmetric Koornwinder polynomials. Based on the form of this construction and numerical evidence, we conjecture a relation between the generating function of the cumulants of the current, and a certain limit of the symmetric Koornwinder polynomials.
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