论文标题
联合$ Q $ - 大型和用于多物种$ Q $ -TAZRP的偏移不变性
Joint $q$-moments and shift invariance for the multi-species $q$-TAZRP on the infinite line
论文作者
论文摘要
本文提出了一种用于计算多物种$ q $ -tazRP（完全不对称零范围过程）中某些粒子位置的新方法。该方法基于该过程的分解为其离散的嵌入式马尔可夫链，该过程更普遍地描述为在渐变部分有序集合上的单调过程。以及指数级随机变量的独立家族。进一步的成分是针对$ q $ -tazRP的过渡概率的明确轮廓积分公式。该方法的主要结果是无限线上多物种$ q $ -tazRP的偏移不变性。 通过先前已知的马尔可夫二元性结果，这些粒子位置与关节$ q $ - 大小写相同。一个特殊的特殊情况是，对于步骤初始条件，订购了$ n $ species $ q $ -tazRP的多点intot $ q $ - tazrp匹配$ n $ n $ -point toint $ q $ q $ - 单物体$ q $ -tazRP。因此，我们猜想通风的$ _2 $进程描述了多物种$ q $ -tazRP的联合多点波动。 作为此结果的概率应用，我们找到了针对扩散缩放制度中多物种$ q $ -tazRP的$ q $ tazRP的显式轮廓积分公式。
This paper presents a novel method for computing certain particle locations in the multi-species $q$-TAZRP (totally asymmetric zero range process). The method is based on a decomposition of the process into its discrete-time embedded Markov chain, which is described more generally as a monotone process on a graded partially ordered set; and an independent family of exponential random variables. A further ingredient is explicit contour integral formulas for the transition probabilities of the $q$-TAZRP. The main result of this method is a shift invariance for the multi-species $q$-TAZRP on the infinite line. By a previously known Markov duality result, these particle locations are the same as joint $q$-moments. One particular special case is that for step initial conditions, ordered multi-point joint $q$-moments of the $n$-species $q$-TAZRP match the $n$-point joint $q$-moments of the single-species $q$-TAZRP. Thus, we conjecture that the Airy$_2$ process describes the joint multi-point fluctuations of multi-species $q$-TAZRP. As a probabilistic application of this result, we find explicit contour integral formulas for the joint $q$-moments of the multi-species $q$-TAZRP in the diffusive scaling regime.
