论文标题
非对称粒子系统的Q-正交二元性
q-Orthogonal dualities for asymmetric particle systems
论文作者
论文摘要
我们研究一类具有不对称相互作用的相互作用粒子系统，显示了自偶性特性。 The class includes the ASEP($q,θ$), asymmetric exclusion process, with a repulsive interaction, allowing up to $θ\in \mathbb{N}$ particles in each site, and the ASIP$(q,θ)$, $θ\in \mathbb{R}^+$, asymmetric inclusion process, that is its attractive counterpart.我们扩展到对对称过程中[8]中所做的正交双重性能的不对称设置。该分析导致Krawtchouk多项式和Meixner多项式的多元$ q- $类似物分别用于广义不对称的不对称排除过程及其不对称包含版本的正交双重性函数。我们还展示了$ q $ -krawtchouk正交关系如何用于计算ASEP的指数矩和相关性（$ q，θ$）。
We study a class of interacting particle systems with asymmetric interaction showing a self-duality property. The class includes the ASEP($q,θ$), asymmetric exclusion process, with a repulsive interaction, allowing up to $θ\in \mathbb{N}$ particles in each site, and the ASIP$(q,θ)$, $θ\in \mathbb{R}^+$, asymmetric inclusion process, that is its attractive counterpart. We extend to the asymmetric setting the investigation of orthogonal duality properties done in [8] for symmetric processes. The analysis leads to multivariate $q-$analogues of Krawtchouk polynomials and Meixner polynomials as orthogonal duality functions for the generalized asymmetric exclusion process and its asymmetric inclusion version, respectively. We also show how the $q$-Krawtchouk orthogonality relations can be used to compute exponential moments and correlations of ASEP($q,θ$).
